Three years ago, City claimed their first top-flight title in 44 years under Italian Roberto Mancini but were off the pace during their defence the following season, finishing well behind local rivals Manchester United in second spot.
Last season brought another league crown to the Etihad Stadium in Pellegrini's first campaign at the club, and he said they could not afford to rest on their laurels if they hoped to avoid another letdown.
"This team won the title two years ago and the next season was a disaster, it wasn't a useful year for anyone," the Chilean said.
"Last season, Manchester United had a disaster (finished seventh) after winning the title.
"It's important from the beginning that we understand we won the title last season and need to win again this year."
City were not at their thrilling best at St James' Park, with some players not up to full fitness and Newcastle showing some steel that was missing for much of last season.
Fernando, a new arrival from Porto, was confident on his midfield debut and with Eliaquim Mangala, Bacary Sagna, Willy Caballero and Frank Lampard not featuring, Pellegrini was confident he had the squad depth to claim repeat Premier League titles for the first time.
"It's very difficult to compare each year. Maybe last year a lot of people doubted we could win the title because it was my first season here in the Premier League," Pellegrini said.
"Today, we have one year more working with the players and we have a strong squad.
"You have five or six teams that can win the title, so we need the same attitude, the hunger with which we have started the season and the same humility in every game.
"I am sure this squad can fight, and we will see at the end of the season which titles we will win."
Dzeko scored 16 league goals last season, and while he did not open his account on Sunday, his clever backheel to set up Silva was the highlight of a strong performance.
"That's why he is renewing his contract here - he has a very important duty in our team. I don't think it's 100 percent finished - but, yes, he will renew his contract. He's a very important player for us," Pellegrini added.
"Today he was one of our best players, not just because of the way he created the first goal and worked hard but because he won a lot of headers and duels and held the ball up well. It was a complete performance."
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