Michael Essien put the Blues in front in the 13th minute and Nicolas Anelka struck twice in five minutes (24, 28) to put the Blues in control at half-time.
Daniel Sturridge added a fourth three minutes after the re-start before Tomas Oravec scored a consolation goal in the 55th minute.
But Ancelotti was more than happy with his team's efforts even though Oravec's goal was the result of Petr Cech failing to catch a cross.
"Every game in the Champions League is hard to play," said Ancelotti. "We started very well in the first half, we played fantastic football, the second half was different.
"Zilina put more pressure on our defence. The back four did a good match. When you are 3-0 up it's normal to have more difficulty.
"The key was Anelka, he played a fantastic game. He created space, he had opportunities, he was the key for this game.
"He can play the position in front, sometimes we use him more wide, sometimes he plays in the middle but he shows the same skills if he plays wide.
"I think that Petr could do better with the goal we conceded but we faced a lot of crosses. We had to put more pressure on the wide side. Defensively the back four had a good game.
"I hope to watch my team play a fantastic game for 90 minutes. Obviously I was a player so I know sometimes there are difficult times, the opponent can come back in the game.
"If I have to judge the performance I am very happy because it's not easy to win 4-1 away in the Champions League.
"I am happy Sturridge scored, but he has to improve his positioning, I would like him to play more infield rather than out wide. He showed fantastic movement to score, I am happy with his performance."
Chelsea have now scored 21 goals so far this season and conceded just two in all competitions but Ancelotti insists they are not looking to beat their 142-goal tally of last season.
"Our aim is to play good football, to win the game," he added. "We are not interested in beating the score from last year because it's our record, maybe we are not able to improve on our record.
Zilina coach Pavel Hapel was surprised by the scoreline and said the only difference between the two sides was Chelsea's clinical finishing.
"I am not disappointed with tonight's game," said Hapel. "We played well and attacked Chelsea. We managed to score so it was okay.
We kept up with Chelsea as much as we could but I am disappointed with the productivity. The score was a surprise tonight.
We didn't show the same productivity in front of goal as Chelsea did."