Lampard had been due to link up with MLS side New York City at the end of a short-term spell with the Premier League champions on New Year's Eve, though his deal at the Etihad Stadium was extended until June on Wednesday.
The decision has caused anger among fans of the American club but Lampard proved his worth to Pellegrini by scoring the winner in Thursday's 3-2 victory over Sunderland.
The Chilean was quizzed further after the win about whether Lampard could head Stateside before the end of the season and also whether the veteran midfielder will play in the Premier League next season.
Asked whether City's progression in the UEFA Champions League affected the arrangement, he said: "No, no. When you ask me before we qualify for [the last 16 of the] Champions League whether there was a link between the situations, Frank and the future I said no.
"Frank knows exactly what I think about that. It was very important to [extend the deal] and he will stay here now for the rest of the season.
"In mid-May maybe you can start thinking again about what might happen in the future.
"Now, he will stay with us until May."
New York City fans group The Third Rail voiced their discontent at the arrangement on Wednesday, stating that many of their members were "outraged" that Lampard would not play in opening stages of their debut MLS season.
Pellegrini sympathises with those frustrations but explained it was in the best interests of all parties for the former England man to stay where he is for now.
"I understand perfectly, they want to see Frank playing," he added.
"To see Frank Lampard play in New York City is an amazing thing. I hope he will be there next year.
"In this moment, I think the best decision for him, for the club and for New York is to stay here with us."
