The Belgian, who re-signed for the club last summer, also said he would like to return to Inter Milan in the future.
The interview caused uproar among Chelsea fans.
Tuchel was also unimpressed and did not select Lukaku in their squad to face Liverpool on Sunday.
The German revealed on Tuesday that Lukaku apologised to the coaching staff and teammates.
Lukaku has now apologised publicly to Chelsea fans in an emotional video posted by the club. Watch it below…
He said: “To the fans, I’m sorry for the upset that I caused. You guys know the connection I have with this club since my teenage years. I totally understand you guys being upset.
“Obviously it’s up to me now to restore your trust and I’ll do my best to show commitment every day on the training ground and in the games.
“To the manager, I apologise. To my teammates and to the board. It was not the right moment. I want to move forward from this and make sure we’re winning football games and I’m performing for the team in the best manner.”
Lukaku signed a five-year contract with the club in the summer and he has reaffirmed his intention to win trophies with the club in the coming years.
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He continued: “They don’t need to question that [commitment]. At the end of the day, I always said I wanted to come here to be successful, that’s why I signed a five-year deal. I think Chelsea as a club is equal to success.
“I think all the players who come here are winning and I have a special passion for this club and I want to achieve that with this football club and want to win here for many years.
“That’s why I signed a five-year deal and I want to make sure I show my commitment in training every day and in games for this football club.”
Lukaku trained with the squad on Tuesday and will be part of the squad for the club’s Carabao Cup semi-final first leg tie against Tottenham on Wednesday evening.