The 32-year-old was withdrawn midway through the second half, in what the Chelsea manager said was a tactical decision, but it was later confirmed the fullback had also picked up a rib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, but acknowledged that the Blues had yet to determine the severity of the problem.
"We need to assess Ashley but hopefully he is fine for the national team," the Portuguese 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."
Focusing on his own team's peformance, Mourinho heaped praise on substitute Willian after the Brazilian came off the bench to score a spectacular maiden Chelsea goal, wrapping up all three points for the visitors in the process.
"His goal is good for the boy," the two-time Champions League winner said. "It’s difficult to arrive when the season has 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 expressed his disatisfaction at a chance the former Newcastle forward had missed early in the second half.
"Demba did what I expected him to do," Mourinho said. "In this kind of match, very direct, small pitch, very British, I thought it would be better to start Demba than Samuel 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 canceling out Oscar's early strike, goals from substitutes Eden Hazard and Willian secured Chelsea a 3-1 victory, a result that sees the Blues leapfrog Manchester City into third place in the Premier League table.