The Brazil-born Spain striker, 26, pulled up 10 minutes after coming on as a half-time substitute for Oscar at Stamford Bridge, with the score 1-1.
Didier Drogba came on as a hobbling Costa — Chelsea’s top scorer this season with 20 goals — was escorted off the pitch and down the tunnel by members of the club’s medical staff.
“For sure, with that injury it will be a couple of weeks minimum,” Mourinho told Sky Sports.
Costa has been bedevilled by hamstring trouble for a year, having been forced off after nine minutes of former club Atletico Madrid’s 4-1 loss to Real Madrid in last season’s Champions League final in Lisbon.
He injured his hamstring in Chelsea’s 3-2 win at Hull City prior to the international break, forcing him to withdraw from Spain’s squad for their games against Ukraine and the Netherlands.
But Mourinho defended his decision to thrust Costa back into action.
“If my medical department decides to take four weeks to recover Diego this would not happen, but in football we need risks,” he said.
“I risk sometimes, as a manager, in a result I don’t like. We played more offensive and if the opponent scores, I don’t kill myself for that.
“But in all the scans they did two days ago the muscle was clear, the image was clear and the player trained twice 100 percent, when he did much more than he did today.
“We put him in dozens of actions and the result was correct. My medical department is fantastic so there is no problem. Next week Remy and Drogba play, and we wait for Costa again.”