The Manchester City boss insists the former Blues midfielder is not 'a traitor' for moving to the Etihad Stadium.
The 36-year-old has joined City on loan this season, ahead of his permanent transfer to New York City FC, who will compete in the next installment of the MLS.
But Manuel Pellegrini insists some have taken their anguish a little too far. Indeed, according to the Chilean, Lampard has done nothing wrong as it was the Blues who decided to part company with him - not the other way around.
"I don't understand the reaction of Chelsea fans that say he is a traitor." he told reporters.
"The problem was not that Frank Lampard did not want to sign another contract at Chelsea. Chelsea didn't want him anymore and he wants to continue playing. He is a competitive player and very important for our team."
The England midfielder's loan move ended a 13-year stay at Stamford Bridge - and John Terry admits it 'does not seem right' to see him in a Man City shirt.
It is a sight Blues fans may have to get used to, however, although Pellegrini confirmed Lampard is not yet ready to take part in Sunday's Community Shield.
That game pits City, the Premier League champions, against FA Cup winners Arsenal in the first competitive action of the new season.