The defending champions maintained their perfect start to the Premier League season with an emphatic 3-1 win at the Etihad Stadium, thanks to two goals from Stevan Jovetic and one from substitute Sergio Aguero.
Even at such an early stage of the 2014-15 campaign, Pellegrini understands the value of winning back-to-back games, having been forced to alter his pre-season preparations due to the World Cup.
"It is important to have six points in the first two games. It was a difficult start for us with some [players] with 15 days working," the Chilean boss told Sky Sports.
"It was important to win, especially to win against [a] strong team like Liverpool.
"I think the way we worked for the whole game, we played a very good team, a very offensive team. We worked without the ball for 95 minutes and, with the ball, [we] did enough to create three goals.
"We were not only patient but played with concentration and intensity. It is a pity they scored a goal but that was a mistake."
The match highlighted Jovetic's quality after the Montenegrin endured an injury-ravaged debut season at the club and Pellegrini was pleased to see the forward doing well.
"He was unlucky with injuries and it was difficult to play two or three games in a row [but] he was patient and has worked hard to come again," the manager enthused.
"I know he's a very good player. I am very happy for him because he deserves it."