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."
After Wednesday's match England coach Fabio Capello said he would speak to Hodgson but was not going to apologise.
That phone call has not yet been made but the Liverpool boss is not too concerned.
"I don't expect apologies from anyone and I'm not prepared to add any fuel to the fire," he said.
"My main concern is with Liverpool Football Club, the match against West Ham tomorrow and in particular with Steven Gerrard.
"He is anxious for it to be put behind him and everyone and not to prolong the discussion."
With Lucas Leiva serving a one-match suspension for his sending-off in last weekend's defeat at Stoke and Jay Spearing injuring his ankle in training this morning, options in central midfield look limited.
The likely option seems to be to pair Christian Poulsen and Raul Meireles together, although another strategy would be to select teenager Jonjo Shelvey.
Defenders Glen Johnson, back after three games out, and Fabio Aurelio, who has made one substitute appearance since the end of August, are both in the squad. Joe Cole (hamstring) is still a week away from fitness.
Scott Parker is a major doubt for West Ham.
The in-form midfielder is suffering with a chest infection and will need a late fitness check as the Hammers look for their first win at Anfield in 47 years.
Julien Faubert returns to the squad after suspension but Valon Behrami (hip) is still a doubt and Manuel Da Costa (ankle), Thomas Hitzlsperger (thigh) and Jack Collison (knee) are ruled out. Young forwards Zavon Hines (knee) and Junior Stanislas (groin) are back in training but will not be risked.
Mexico winger Pablo Barrera believes West Ham "have a great chance" to drag themselves off the foot of the Barclays Premier League with victory at Liverpool.
The Hammers have secured only one win from their 13 games, and the Upton Park faithful were left frustrated following successive draws against West Brom and Blackpool last week.
Under-fire manager Avram Grant continues, for now at least, to have the full support of the board and insists the results which his team's performances merit will come.
Barrera was one player guilty of missing a golden chance to break the deadlock against Blackpool on Saturday, shooting straight at the keeper from 12 yards.
However, the summer signing is optimistic the Hammers' fortunes will soon turn as they go in search of a first victory at Anfield in almost half a century.
"It will be a very difficult match, but we need to start winning," Barrera said.
"The team is playing well despite being frustrated by the results in the recent matches.
"We have a great chance to get something from Liverpool."
Barrera added on the club's official website: "Against Blackpool, we should have won the match. In general the team played very well. We created a lot of chances, but we didn't score.
"We just need to keep working to come out from this period, because I believe that we've got quality in the squad to do it.
"Of course mentally we are not in our best moment because we have not been winning.
"However, the team is playing well, so we just need a little bit extra to turn draws into wins."