However, he has stressed both he and the player, who is out for three to four weeks with a hamstring tear, are keen to put the matter behind them and concentrate on getting the midfielder back to full fitness.
The 30-year-old was due to play an hour in Wednesday's friendly against France but ended up playing 85 minutes before succumbing to injury.
"As Liverpool manager I am frustrated and disappointed to lose such an important player for such a long period of time," said Hodgson.
"Anything I say - other than I am disappointed and even a little bit angry about it - would be dishonest.
"But I know Steven, as an important player for club and country, is keen to put a tin lid on the matter. He is disappointed and sad too but he is going to do everything he can to get back to fitness as quickly as possible."
Source: PA
Source: PA