Everton had previously asked for a retraction of Mourinho's "possibly defamatory" allegations - but Chelsea refused to comment on Monday.
Johnson himself said: "I merely jumped out of the way of Chelsea's goalkeeper as he came out at my feet. I do not consider myself to be a diver."
Johnson, who joined Everton in the summer from Crystal Palace, added: "I was not trying to get a penalty. I have to say that I feel greatly disappointed that my integrity as a footballer has been unfairly questioned.
"I believe the incident highlighted by Mr Mourinho was badly misinterpreted by him. I hope that the Chelsea manager will retract his statement."
On Sunday, after the game, Mourinho had said: "He's dangerous for opponents because you cannot trust him, and I was not happy with that.
"But I think he was a bit embarrassed and he behaved very well after that."
The Chelsea boss stopped short of calling Johnson a cheat but stated: "In my country we call them 'intelligent' players. In other countries you can use different words and are critical.
"I've been in this country for three years now and I am influenced by your culture. It is a country I admire, I am proud to be part of it.
"For me when a player chases a penalty, he is no longer an intelligent player."
Everton boss David Moyes reacted furiously to Mourinho's accusations - clashing with him on the touchline after the Portuguese made a diving motion with his hands.
Moyes said after the game: "He (Mourinho) has got a big 15 stone striker up front who is quite partial to it (diving) himself.
"I saw the incident on television and I don't think it was a penalty but it certainly wasn't a dive either.
We would urge the footballing authorities to look closely at Mr Mourinho's comment and then, perhaps, seek a formal explanation
Joint statement from Everton and Johnson's agent
"A few weeks ago the Chelsea keeper got caught by a Reading player, who was criticised for that.
"Our player is slightly bumped, straddles the goalkeeper and jumps over him. He's missed the keeper and he gets criticised for that, so you can't win."
Everton issued a joint statement with Johnson's agent Anthony McFarlane on Monday.
It read: "To query a player of Andrew's integrity is wholly unacceptable and possibly defamatory. We ask Mr Mourinho to immediately retract his allegations.
"We would urge the footballing authorities to look closely at Mr Mourinho's comment and then, perhaps, seek a formal explanation.
"Both Everton FC and Andrew Johnson have always believed in the virtues of fair play."
It has been claimed that Everton are considering taking legal action against Mourinho because they believe the reputations of the player and the club were damaged by his comments.
According to a report by the Press Association, Everton are aware that Mourinho gave several, slightly different, interviews after the game.
The one they will base their complaint on is the interview Mourinho gave to Sky Sports in which it is claimed he says: "I know he dives."
Everton reportedly have a full transcript of that interview.
BBC: Source
My opinion :Everton are making themselves look like idiots to take legal action over this.
Johnson himself said: "I merely jumped out of the way of Chelsea's goalkeeper as he came out at my feet. I do not consider myself to be a diver."
Johnson, who joined Everton in the summer from Crystal Palace, added: "I was not trying to get a penalty. I have to say that I feel greatly disappointed that my integrity as a footballer has been unfairly questioned.
"I believe the incident highlighted by Mr Mourinho was badly misinterpreted by him. I hope that the Chelsea manager will retract his statement."
On Sunday, after the game, Mourinho had said: "He's dangerous for opponents because you cannot trust him, and I was not happy with that.
"But I think he was a bit embarrassed and he behaved very well after that."
The Chelsea boss stopped short of calling Johnson a cheat but stated: "In my country we call them 'intelligent' players. In other countries you can use different words and are critical.
"I've been in this country for three years now and I am influenced by your culture. It is a country I admire, I am proud to be part of it.
"For me when a player chases a penalty, he is no longer an intelligent player."
Everton boss David Moyes reacted furiously to Mourinho's accusations - clashing with him on the touchline after the Portuguese made a diving motion with his hands.
Moyes said after the game: "He (Mourinho) has got a big 15 stone striker up front who is quite partial to it (diving) himself.
"I saw the incident on television and I don't think it was a penalty but it certainly wasn't a dive either.
We would urge the footballing authorities to look closely at Mr Mourinho's comment and then, perhaps, seek a formal explanation
Joint statement from Everton and Johnson's agent
"A few weeks ago the Chelsea keeper got caught by a Reading player, who was criticised for that.
"Our player is slightly bumped, straddles the goalkeeper and jumps over him. He's missed the keeper and he gets criticised for that, so you can't win."
Everton issued a joint statement with Johnson's agent Anthony McFarlane on Monday.
It read: "To query a player of Andrew's integrity is wholly unacceptable and possibly defamatory. We ask Mr Mourinho to immediately retract his allegations.
"We would urge the footballing authorities to look closely at Mr Mourinho's comment and then, perhaps, seek a formal explanation.
"Both Everton FC and Andrew Johnson have always believed in the virtues of fair play."
It has been claimed that Everton are considering taking legal action against Mourinho because they believe the reputations of the player and the club were damaged by his comments.
According to a report by the Press Association, Everton are aware that Mourinho gave several, slightly different, interviews after the game.
The one they will base their complaint on is the interview Mourinho gave to Sky Sports in which it is claimed he says: "I know he dives."
Everton reportedly have a full transcript of that interview.
BBC: Source
My opinion :Everton are making themselves look like idiots to take legal action over this.
