Blues great Lampard was shown the door this week after a number of poor results in the Premier League.
Rooney says he wasn't surprised by the news given Chelsea's history, but felt sympathy for his former England teammate.
"I wasn't surprised, if I'm being honest," said Rooney.
He's brought players in, which will take time to build his team and to challenge for titles. I don't think they were too far away points-wise from being able to challenge for titles.
"It's obviously disappointing for Frank and his staff, but you're asking me if I was surprised and the answer is no."
Rooney added: "I'm sure Frank would have known that he wasn't going to get time, going in at Chelsea.
"I think they demand trophies, which is good on one sense, it keeps the managers on their toes, and they have to produce, they have to win trophies.
"But if you are going to give someone a project to bring players in from quite a few countries then at least give them the season to see where they're at."