The Blues were undone 3-1 by Wigan in their previous Premier League outing and then struggled to a 1-0 UEFA Champions League victory away to Apoel Nicosia in midweek.
But they moved back to the top of the table courtesy of goals from Nicolas Anelka and Florent Malouda to hand Liverpool their third defeat of the season.
And Ancelotti brushed aside suggestions that he had been feeling the pressure before the Stamford Bridge meeting with the Anfield outfit.
Resolved"In Italy we usually say, 'It's the same the world over'," said Ancelotti. "It was not pressure. We lost one game and played badly for a second match but we worked hard to find the problem and resolve it.
"After this match, we've shown we've resolved our problem. It was not a big problem.
"It was an important win. It's normal that it was difficult because we played a strong team. Above all, the match was difficult.
"We maintained good control during the match. First half, it was a match with a lot of balance. Both teams kept good control of their defensive positions.
"The second half was different. We scored the first goal and had an opportunity to counter-attack. They put a lot of pressure on our midfield and wanted to draw but I think we deserved to win because we did a very good job during the 90 minutes.
"I know we did what we prepared before the game and, for this, I'm happy. We wanted to avoid free passes for Steven Gerrard because he's a very dangerous player. Michael Ballack, Michael Essien and Frank Lampard did that job fantastically.
"They used the right side to attack but, on the left, we did a good job."
Work togetherStriker Didier Drogba did not get on the scoresheet but he made both goals and Ancelotti was delighted with the Ivory Coast international's contribution.
"He did very good support for Nicolas Anelka and worked very hard," he added. "But all the players did.
"If you want to win against Liverpool or other big teams, you have to work together. Chelsea worked together today for each other.
"It was not possible to have space to play against Liverpool, to play football, because they had very good defensive organisation and don't leave space in their midfield.
"Sometimes you can use the strength of Didier, Essien or Ballack. That's a characteristic that we can use sometimes.
"To control Fernando Torres is not easy. Ricardo Carvalho and John Terry did a fantastic job. I think Torres had one opportunity in the first half, and Terry and Carvalho played very well."