Carragher injury completes bad day for Liverpool
The former England centre-back suffered the injury in the closing minutes of the match at White Hart Lane, when Spurs came from behind to win 2-1 with a stoppage-time goal by Aaron Lennon.
"We think Jamie has dislocated his shoulder which is a real blow for us and for him," Hodgson told reporters.
"I don't know at this stage how long Jamie will be out for but I would think it will be quite long because it's a serious injury.
"It's an unfortunate thing to happen on his 450th appearance in the Premier League.
"It is a blow for us. Daniel Agger is still out injured and we are not really that well blessed for centre-halves.
"We are now without Steven Gerrard and Jamie for a period of time - both of whom are the lifeblood of this club."