City were made to work hard at St James' Park but picked up three points thanks to David Silva's goal late in the first half and Sergio Aguero’s stoppage-time strike.
Pellegrini was delighted to start the campaign with a win and picked out the attitude of his players as a key factor in their success.
"It was important to start with a win," he told Sky Sports.
"I think the players were both hungry and humble. We need both those things if we are going to continue winning titles and if we want to improve on what we did last year.
"It was so important to me that the players had that attitude from the beginning to the end of the game."
Pellegrini does not believe his players are yet up to full speed, with many of them returning late to training following the World Cup, but he was pleased they held firm and kept a clean sheet.
He added: "We were very solid at the back and Joe Hart didn't have any problems and in the second half it was normal that we were starting to get tired.
"The players are not able to play 90 minutes at the moment but we continued with our attitude and scored the second goal."