Cole was withdrawn midway through the second half, in what the Chelsea manager admitted was a tactical decision, but it was later revealed the full-back had picked up a rib injury during the game.
After the game Mourinho did not rule Cole out of England's crucial World Cup qualifiers against Montenegro and Poland, conceding the Blues did not yet know how bad the damage was.
"We need to assess Ashley but hopefully he is fine for the national team," Mourinho told reporters after the game.
"I didn’t know he was clutching his ribs when I did it [brought him off]. But it was a tactical decision. He will go for a scan when we get back. I hope he is fine. I want England to do well so I hope he is ok."
Focussing on his own team's peformance, Mourinho reserved praise for substitute Willian, after the winger came off the bench to score a spectacular maiden Chelsea goal, wrapping up all three points for the Blues in the process.
"His goal is good for the boy," Mourinho said. "It’s difficult to arrive when the season’s started already and it’s difficult to arrive when from a different league, so step-by-step he is doing well."Mourinho shocked many by starting Demba Ba ahead of Samuel Eto'o in attack, but the Senegalese forward justified his inclusion almost immediately, setting up Oscar for Chelsea's opener after just three minutes.
However, when justifying his decision to start Ba after the game, Mourinho could not his disatisfaction at a chance Ba had missed early in the second half.
"Demba did what I expected him to do," Mourinho explained. "In this kind of match, very direct, small pitch, very British, I thought it would be better to start Demba than Samuel [Eto’o] as he’s more physical.
"He has to score in the first minute of the second half though. I think it is an easy goal. He puts the ball in, it’s 2-0, we all go home and no heart attack at the end.
"After that, by not scoring, we left the door open for them. They scored and we were in trouble."
Despite Anthony Pilkington cancelling out Oscar's early strike, goals from substitutes Eden Hazard and Willian secured Chelsea a 3-1 victory, a result which sees the Blues leapfrog Manchester City into third place in the Premier League table.