The 32-year old is expected to spend up to six weeks on the sidelines and his injury couldn't come at a worse time for Hodgson whose defence has been questionable this term.
Sunday's last-gasp winner, scored by Spurs winger Aaron Lennon, came when Carragher was off the pitch and Hodgson is clearly concerned about the future.
"I'm very disappointed, especially as the winner came at a time when we had to reorganise our defence with Jamie off the pitch," he said.
"It was cruel to come away with nothing having lost our talismanic centre-half - and then paid the price for not dealing with a routine long ball."
Hodgson's comments were compounded when new Reds defender Paul Konchesky admitted he is not up to the level required of him at Anfield.
"I've got to up my game. Where I've played before has not been as high a standard as Liverpool, but this is a good pressure," said Konchesky.