The 50-year-old Belgian was relieved of his duties on Sunday, 16 months after being appointed following stints in charge of Genk, Club Brugge and Monaco.
Rodgers, who has never failed to win the Premiership title across his two spells in charge of Celtic, acknowledged that Clement had ultimately paid the price for being unable to get Rangers ahead of his own side during his time in the Ibrox hot seat.
“Like it is for any manager, I’m always disappointed when a manager loses his job,” Rodgers said on Monday.
“Obviously, Philippe has been in there for the period of time that he has. I’m disappointed for him as a coach. I think we all know the conditions up here. You have to be winning and show that consistency to win.