A Nicolas Anelka double put Chelsea firmly in command of the tie and the Blues now look favourites to go into the quarter final stages.
And Ancelotti is adamant that Chelsea's season is not over yet.
"We are still alive," The Chelsea manager told Sky Sports.
"It was a good result and good performance, we were very well prepared and focused but it is just the first half there, is a long way to go.
The Chelsea boss admitted he had been feeling the pressure after recent results, which have seen the Blues slip into fifth in the league -having failed to score against Fulham and Liverpool in previous matches.
A defeat to Everton on penalties on Saturday meant even less chance of some silverware after being knocked out of the FA Cup, but the Italian conceded it was a relief to get the victory in Denmark tonight.
"Obviously, it is very satisfying having had a considerable amount of pressure put on us to get a good result, we want to do the best and tonight was good," Ancelotti continued.
Fernando Torres made his Champions League debut for Chelsea but was unable to open his account for the Blues despite having a few chances to do so.
Ancelotti however felt that Torres played a significant part in the result and played very well, even opting to take Anelka - who was on a hat trick at the time - out of the action before he substituted the Spaniard in stoppage time.
Although the Chelsea boss argued it was because Torres had not played on Saturday and Anelka needed a rest after being involved in extra time at the weekend.
"No, because Torres did not play Saturday [against Everton]," Ancelotti explained.
"Anelka played extra time on Saturday, and Torres was fresh.
"Anelka did a fantastic job by scoring two goals but Torres was key of this game, he is a striker and always is dangerous.
" He was unlucky that he did not score but he still had a fantastic game."
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