Lukaku was star performer at the Club World Cup where his two goals were crucial to Chelsea being crowned world champions.
Asked if the club will take disciplinary action against the striker, the gaffer said “We will do it behind the close door and we will do it openly.”
Saturday’s win places City second on the league table, leading Chelsea on goal differences.
Tuchel’s Chelsea have defeated Pep Guardiola’s Manchester City in their last three meetings.
Mr Tuchel funded the heart surgery on knowing his housekeeper was working overtime to pay for it.
Chelsea held Liverpool to a 1-1 draw at Anfield in their English Premier League game on Saturday.
The Chelsea quartet received honours for their sterling showing at last season’s UEFA Champions League campaign.
Belgian striker Romelu Lukaku has signed a five year deal with English Premier League side Chelsea.
In 30 games with Tuchel in charge, Chelsea won 19 games in all competitions, winning Champions League and placing fourth in the Premier League.
A first half goal by Chelsea’s record signing, Kai Havertz, was enough to deny the Citizens their first champions League trophy.
