Manchester United boss Mourinho spoke at length to Conte at the final whistle of Sunday's defeat to his former club, with suggestions the Portuguese had been annoyed that his Italian successor had encouraged the home support to cheer on the Blues when they were already 4-0 up.
Reports in Italian media said Mourinho, who has a history of touchline indiscretions, told Conte: "You don't celebrate like that at 4-0, you can do it at 1-0, otherwise it's humiliating for us."
Conte insisted he had moved on as Sunday's win is now in the past.
But, speaking ahead of Wednesday's EFL Cup fourth round clash at West Ham, he made a pointed remark, which may have left Mourinho with his ears burning.
"I think that everyone must show respect for me, for my work, for my job," Conte said.
"In every game I show myself
Not here, only one game
I have a history and you can see my history, my past and my behaviours on the bench.
"I'm a passionate man, I show this in the past (and) now
I want to stay very close to my players, also to play with them, to help.
"I always show respect for the opponent, for the other teams, for the other club and my history speaks for me."
Conte is looking forward to playing at the London Stadium, with its vast technical areas comparing favourably to Stamford Bridge's small space for a man who kicks every ball and bellows to his players from the touchline.
Conte, still hoarse following Sunday's win over United, was asked whether his behaviour could antagonise opposition fans.
The former Juventus boss preferred to focus on the positive atmosphere, rather than the potential for trouble in the derby with the Hammers.
He added: "I know that these two teams are big rivals, but in England it's fantastic the atmosphere during the game, during a match and I hope to see this tomorrow.
"If I have to compare the technical area to Stamford Bridge, I'm happy.
"For me it's very difficult
I have to ask my club to try to change the technical area
My area and also for the other coach."
Captain John Terry was an unused substitute in the wins over Leicester and United, but could start for the first time in six weeks following an ankle injury as Conte prepares to rotate his options.
"John is fit," Conte said
"He's fit to start
He's in good shape, but tomorrow I decide the starting XI."
Willian came off the bench against United and could start for the first time since taking compassionate leave following the death of his mother.
The likes of midfielders Nathaniel Chalobah could also start, but Conte's priority is to pick a team strong enough to win.
He added: "It's important to arrive at the right message
Tomorrow we want to win.
"Then, if I decide to put in the team, in the starting XI some young players, it's only because I trust in these players, not to gift (an appearance).
"This cup is an important cup for us
(But) this season we have only FA Cup and this cup to see the other players.
"For this reason tomorrow we can see probably some changes."
Defender Kurt Zouma played 45 minutes for Chelsea's development side on Monday and is likely to return to full training with Chelsea's first team on Thursday.
Branislav Ivanovic is back in training but Cesc Fabregas (thigh) remains out.
Source : PA