The 39-year-old Keane, who had been at Ipswich since April 2009, left with the Championship club 19th in the table after seven defeats in their last nine games.
Ancelotti has not forgotten the night in Turin in 1999 when Keane scored for Manchester United in the Champions League against his Juventus side at the Delle Alpi.
"I was excited about the chance to meet Roy Keane for a long time because I was the manager of Juventus when he gave me disappointment because he scored in the semi-final of the Champions League," Ancelotti told reporters on Friday.
United trailed 2-0, and 3-1 on aggregate, before fighting back to win with goals from Keane, Dwight Yorke and Andy Cole. They went on to win the trophy and complete the treble.
"Now I don't have the chance to meet him and I am sorry for this because when a manager loses his job it is not a good moment, but this is the life of the manager," said Ancelotti.
"The manager has to be able to cope with this moment. It is not good but hopefully he can move forward quickly."
Ancelotti is himself under pressure after a dismal run in which his side have picked up just 10 points from 11 matches and slid from top spot to fifth place in the Premier League.
"In football, usually we say when everything is okay the players are fantastic and when everything is wrong it is the manager who is not so good," he smiled.
"But we know this. When the moment is not so good the manager has to take more responsibility than the others. At the moment, I feel more responsibility than my players and this is normal, this is not a worry for me."
Chelsea's dramatic slump in form has left them nine points adrift of Manchester United and the champions have also played a game more than the league leaders but Ancelotti is hoping the distraction of the FA Cup can provide salvation.
"The good thing is in the FA Cup and the (last 16 of the) Champions League we don't have a gap to close," he said. "We have the same possibility as the other teams and maybe this could give to us plenty of motivation."
Chelsea face FC Copenhagen in the Champions League next month.
