Lampard was sacked on Monday morning.
Former Chelsea coach Rodgers said later in the day: "I am really sad for him and his staff. I know how much the club means to him and all he's given them.
"Looking at the squad, looking at everything else around it and how young they are, the adaption for players coming in, it's a team and a squad that needs time. Unfortunately he hasn't been given that time.
"I really feel for him. He had the courage to step out of an amazing career as a player and could have taken an easier route and went straight into coaching and managing.
"He took a job he couldn't really turn down, even though he had not a lot of experience. He thought he could do a great job there and I thought he did do that last season.
"Ok, results wouldn't have been what they wanted (this season) but it's not what he wanted because he's a winner himself. But like I said, I feel it is a job that needed time and sadly for him he doesn't have that time."