Only 24,973 supporters turned up to watch the match against the Norwegians and they made their feelings known at the final whistle by giving Mourinho and his men a chorus of dissent.
Despite peppering the Rosenborg goal with more than 25 shots, hitting the woodwork on two occasions, Chelsea failed to find a winner.
"I have some sympathy with the fans. We have to be beating teams at home, whoever it is. You understand their frustration," said Cole.
"We are getting chances but maybe not taking them or passing at the right times, so the jeering is fair enough.
"We should kill off teams and win these kind of games. Maybe there is a lack of confidence from a few players.
"We have only scored first in the Premier League against Portsmouth this season and we are disappointed at how that is going.
"We are conceding silly goals from free-kicks a lot which, for a team like us with the players we have got, we shouldn't be doing.
"Jose Mourinho did not say anything to us as the end of the game but we all know that he was got to be disappointed.
"We are disappointed with how it went and on Sunday (Manchester United away) we have to change that."