Cech ended his 11-year association with Chelsea by joining London rivals Arsenal after being consigned to a bench role behind Thibaut Courtois at Stamford Bridge last season.
Begovic, who was recruited to fill the void left by Cech, is set to be thrust into action against Manchester City following Courtois' red card during Chelsea's 2-2 draw at home to Swansea City and Mourinho has complete faith in the Bosnian in the absence of Chelsea's regular number one.
"We don't miss Petr," Mourinho said. "We've got a good keeper, the problem with Petr is not that we miss him because we have two excellent keepers.
"The problem with Petr is that an opponent is better than before.
"Thibaut and Asmir are two fantastic keepers. My club did very well by getting a keeper on time and not on August 31.
"If my club gives me a keeper on August 31, then we have a problem not just for today but also for the next match. Unless the people understand that it's not a red card and they clear the suspension."