Martinez felt fatigue from the midweek international fixtures played a part in their second-half performance but losing Ben Watson to a broken leg did not help.
The 27-year was caught just above the shin by Reds winger Raheem Sterling's knee as they jumped for a ball in the first half.
"He has a fracture and we are going to assess him now because maybe he will require surgery," said the Spaniard. "If he needs surgery he will probably be out for four months and that will be a major blow for us.
"The injury affected us too much because I thought we started quite sharp and controlled the game in the first half.
"I thought we were the team who looked like being a real threat and I thought we stopped Liverpool completely. Unfortunately in the second half we suffered too much from the international fixtures.
"The first goal we gave it away - it was one of those days as nothing went our way.
"The second goal went in and the third goal came from a throw-in which should have been our ball. We attracted all sorts of bad decisions and bad luck."