City - who had won 19 of their previous 20 matches in all competitions - started Monday's clash strongly, but Chelsea slowly worked their way into the game and sealed a 1-0 win thanks a superb Branislav Ivanovic strike just after the half-hour mark.
Jose Mourinho's side went on to hit the woodwork on three occasions as City's goal lived a charmed life, while at the other end the hosts struggled to test Chelsea keeper Petr Cech.
The result represents the first time since November 2010 that City have not scored at home in the Premier League, a run of 61 matches, but Pellegrini is confident his side can recover - even though Chelsea are now level with them in second place in the table.
"For Chelsea it was a decisive game, for us it was an important one," the Chilean told Sky Sports. "We're still two points behind Arsenal.
"It was a very tough game, they score a beautiful goal but we had clear chances at least to draw.
"We couldn't do and they had two or three chances against the post. It was a very close game, they played well.
"We are not going to have any problems (bouncing back)."
City were dealt a blow before kick-off with an injury to Fernandinho - and Pellegrini admitted their task was made harder without their Brazilian midfielder and other high-profile absentees.
"Missing players (made it tough)," he added. "To play without Sergio Aguero, Samir Nasri, Fernandinho and Javi Garcia was difficult.
"Fernandinho was a big loss."
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