The 25-year-old, who starred for the British & Irish Lions last summer, kicked all 18 of Wales' points against the Red Rose in the 29-18 defeat before being helped off the Millennium Stadium pitch.
Halfpenny flung himself into the path of the onrushing wing Luther Burrell to deny England a third try, but now looks set for a lengthy spell on the sidelines.
"Leigh's dislocated his shoulder so I think that's him gone for the rest of the season," Gatland said.
"I think we hurt ourselves by the number of turnovers we conceded. We didn't retain the ball for long enough periods.
"We were on the wrong side of the ledger with the scrum penalties. But England deserved to win the game. Credit to them. They played pretty well."
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