Other than apologising in private during his meeting with Tuchel on Monday, Chelsea released a video of Lukaku apologising directly to the club's supporters on Tuesday night.
Lukaku said: "To the fans I'm sorry for the upset that I've caused. You guys know the connection I have with this club since my teenage years, so I totally understand you guys being upset.
"Obviously, it's up to me now to restore your trust and I'll do my best every day to show commitment on the training ground and in games to make sure we win games.
"And also to the manager, my team-mates and the board, I apologise, because I think it was not the right moment, also.
"And I want to move forward from this and make sure that we start winning football games and make sure that I start performing for the team in the best manner."
On the battle Lukaku faces to try to win back the faith of the Chelsea fans, Tuchel said: "He cannot expect now everybody to be super happy the next day, but he is still our player, and we have good reasons and a lot of reasons to make him play for us. There are zero doubts about his commitment to the team and the club.
"In the end, it is also very important that the stadium supports the team. Even if somebody has a different opinion on it or strongly disagrees, it is about the team in anything we do. We are in a moment where we really need the support."
Lukaku insisted that he is committed to Chelsea, following his £97.5million move from Inter Milan, but conceded he had not been clear enough about that during the interview that caused so much anger.
"I think I should have been much clearer in my message to be honest," said Lukaku. "Because the interview was about saying goodbye to the Inter fans, it was not about trying to disrespect the (Chelsea) fans, the football club, the owner, my team-mates, the technical staff. Because they made a lot of effort for me to come back here and I wanted to come back here.
"I was on a mission to come back since I left, so I totally understand the frustrations of the fans. But now it's on me to make sure my commitment is at 100 per cent and I will do that in every game.
"My club was Chelsea, everybody knows that from being 10 or 11 years old I said I wanted to play for Chelsea. There were clearly images when I came on my school trip that I said I wanted to play for Chelsea.
"So, for me, I came here when I was 18 and it didn't go so well. Now I'm back at 28 in the prime years of my career - I can't really mess this up. I miss my family. I miss my mum, I miss my boy. They are moving in soon. Hopefully, I can enjoy life more when they are here."
Asked if Lukaku was his first-choice signing, Tuchel said: "Yes, of course. First choice is always about what's possible and what's not possible, and what is a good fit.
"It was the perfect fit and it still is, and we have to prove it, I have to prove it, he has to prove it. Let's say the spotlight got a bit brighter on him now.
"I don't think you can assume that we spent this amount of money and we bring all this effort while having major doubts or having second thoughts, or having him on the list in place number four."
Reports in Spain have claimed Real Madrid have cooled their interest in Antonio Rudiger, whose representatives have claimed to have opened talks with the Spaniards and a host of other European clubs, with the defender now in the final six months of his Chelsea contract.
