Cole limped off with a hamstring injury in the first half of Monday's 1-0 victory over Manchester United in an FA Cup quarter-final replay and Cahill was already ruled out for two weeks because of a knee injury.
"The problem now is that Cahill will be out for another 15 days at least and Ashley the same," interim manager Rafael Benitez told reporters after Demba Ba's exquisite second-half goal gave Chelsea victory.
"Our squad is not too big but we can manage if we don't have injuries. You have to approach every game carefully, make substitutions or rotate players - sometimes it will go well, sometimes not so well."
Monday's game was the second for Chelsea in less than 48 hours, following Saturday's 2-1 Premier League defeat at Southampton.
Benitez made seven changes against United and will need to continue to rotate with Thursday's Europa League quarter-final first leg against Russians Rubin Kazan coming up, quickly followed by Sunday's Premier League game against Sunderland.
Chelsea are set to visit Rubin for the second leg on April 11 before taking on Manchester City in an FA Cup semi-final at Wembley three days later. They then meet neighbours Fulham in a Premier League game on April 17.
"It was very important for everyone to win today," said Benitez. "This was a great game and a great victory for us.
"The priority is to finish in the top four in the Premier League but we have to approach every competition trying to win. We've had two games in less than 48 hours so we had to manage the squad.
"Before last week's international break we played against United, Steaua Bucharest and West Ham and we were the best team in the world," he said, referring to Chelsea's run of one draw and two wins.
"Then we lost against Southampton and we were suddenly the worst in the world. You have to have a balance."
