Cole's contract at Stamford Bridge expired at the end of June and he has subsequently left the club as a free agent after failing to reach a new agreement with the Blues.
Ancelotti admits he is disappointed to have parted with a player of Cole's calibre, but claims the situation had nothing to do with him.
"The problem was economic," said the Italian.
"It was a problem between the club and Joe Cole, not me. We spoke about this but when the problem is with money, it is not my problem.
"It is difficult to keep a player all the time in one squad.
"I think Joe Cole, like Michael Ballack and Julian Belletti, did a fantastic job. I want to thank them but now is the time to change."
Ancelotti, who guided Chelsea to a Premier League and FA Cup double last season, is hoping his side can push on in 2010/11 despite seeing considerable experience head through the exits.
He has also revealed that the Champions League will be a top priority after they fell at the last 16 stage to Inter Milan last term.
"Our aim is to do better than last year in the Champions League," added Ancelotti.
"We went out too early last season. It is not easy to be competitive in every competition.
"If it's possible then we want to repeat what we did last year in the other competitions."
Cole has been linked with Arsenal, Tottenham, Manchester United and Manchester City since the season ended, with Liverpool the latest club said to have enterered the race to sign him.