The Black Cats are just one point above the relegation zone in the Premier League, having failed to register a win since January 16, following their 1-0 defeat to league leaders Manchester United on Saturday.
"I was shocked like everybody else at what had happened," Lambert told Sky Sports News. "I was shocked.
"Nobody is safe. I had the privilege of working under him for five years and it was fantastic.
"If you make that change, you'd think someone is going to be appointed pretty quickly there at this stage of the season."
Sunderland travel to Stamford Bridge to face Chelsea in their next match.