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Lukaku was left out of Chelsea's Premier League squad on Monday (AEDT) for the 2-2 draw with Liverpool as punishment for comments made in the Italian press.
In a wide-ranging discussion, Lukaku said he was not "very happy with the situation" at Chelsea and expressed a willingness to return to Inter Milan someday.
Rumours suggested the Belgium international could be heading for a Stamford Bridge exit, but Tuchel has since confirmed Lukaku returned to training after talks the previous day.
Lukaku has now come out to address the matter in public in an attempt to put the issue to one side.
A message from Romelu.— Chelsea FC (@ChelseaFC) January 4, 2022
"To the fans, I'm sorry for the upset I have caused," he said in an interview published by Chelsea's website.
"You guys know the connection I have had with this club since my teenage years, so you know I totally understand you guys being upset.
"Obviously it's up to me now to restore your trust, and every day I will do my best on the training ground and in the games to try to help us win.
"To the manager I apologise, and to my team-mates and the board because I think it was not the right moment also.
"I want to move forward from this and make sure that we start winning football games and I can help the team in the best manner."
Lukaku revealed in the previous interview that he would one day like to return to Inter, where he enjoyed playing under former head coach Antonio Conte.
The striker's comments were met with disdain by Inter fans, but Lukaku has tried to clarify why he agreed to the interview in the first place.
"I should've been much clearer in my message to be totally honest," he continued.
"The interview was about saying goodbye to the Inter fans, it was not about trying to disrespect the [Chelsea] fans and the football club, the owner, my team-mates and the manager.
"They made a lot of effort to bring me back here and I wanted to come back here, I’ve been on a mission since I left.
"They [the fans] don't need to question [my commitment]. I always said I wanted to come here and to be successful, that's why I signed a five-year deal. I think Chelsea is a club that equals success.
"All the players that come here come for winning and I have a special passion for this club. I want to achieve that with this club, I want to win here for many years. I want to make sure I show my commitment every day.
"There are images when I came with my school on a trip that I wanted to play for Chelsea. I came when I was 18, it didn't go so well, now I'm back at 28 in the prime years of my career, I can't mess this up.
"I worked hard for the last 10 years to get this opportunity and I'm really happy to be here."
Lukaku, if selected, will look to redeem himself on the pitch against Conte's Tottenham on Wednesday in the first leg of their EFL Cup semi-final.