Lampard, 36, has joined City on loan from MLS side New York City until the new year after ending his 13-year stay at Chelsea in pre-season.
The midfielder, who called time on his England career last month, was a substitute at half-time as he made his debut in the 2-2 draw at Arsenal last week.
But after he scored a goal that prevented City from falling eight points behind in the title race, Pellegrini was expecting more of the same in the next three months.
“When I spoke with Lampard, it was not to make him a favourite to stay at Manchester City, it was because I was absolutely sure he will be a very useful player for our team,” the manager explained.
“He has nothing to do in New York until January when they start the season there.
“It was very important for him to continue working every day and playing in our team but also it was very important for our team to have a player with the experience and quality of Frank Lampard.”
Chelsea looked set to pick up an important win when substitute Andre Schurrle turned in from Eden Hazard’s cross shortly after City’s Pablo Zabaleta had been sent off at Eastlands on Sunday.
But seven minutes after coming off the bench, Lampard scored with a typical late run into the box as he turned in James Milner’s cross to earn a point.
Pellegrini was critical of Chelsea’s approach, describing them as playing like a “small team” and comparing them to Stoke.
“It think we played 90 minutes against a small team trying to defend, trying to keep 10 players in front of their goal, and (we were) a team that wanted to win from the beginning,” he said.
“I think we played against exactly the same team we played against Stoke here.”
– Mourinho not taking bait –
Chelsea boss Jose Mourinho refused to rise to the bait and, after seeing his team drop points for the first time this season, declared himself happy with his team’s position at the top of the table.
“It’s one point won because we arrived here leaders with two points more than second and we leave the stadium with a three-point lead.
“I don’t look to direct opponents, I don’t look to other clubs in a special way. I look to the table and we are leaders by three points,” the Portuguese manager added.
“We come here to a super-difficult stadium and a super-difficult opponent and we leave to better conditions than we arrived, so good.”
Mourinho has regularly criticised Pellegrini since taking over from the Chilean at Real Madrid in 2010 and, as well as mispronouncing his name on two occasions, he hit back at the City manager.
“Pellegrino, many times he says he never speaks about me and my team but he keeps doing the same thing. I am the one that does as he says.
“I don’t comment on his words. Don’t ask me about his words, I am not interested in that.”
Pellegrini added he has no concerns about City’s start to the season despite the club going four games without a win for the first time in four-and-a-half years.
The Premier League champions are five points behind Chelsea.
City, who were beaten 1-0 by Bayern Munich in their opening match of this season’s Champions League match last week, have lost ground in the English title race with a 1-0 defeat by Stoke and a 2-2 draw with Arsenal preceding their point against Mourinho’s table-toppers.
“I think that in the way we played (against Chelsea), maybe we are not taking the points that we deserved but I am not concerned about the way we played,” said Pellegrini.