However, most of the focus was on the increasingly precarious position of Hodgson, who is in his first season at the helm after succeeding Rafael Benitez in July.
As the curtain came down on a third defeat in four league games for the Reds, leaving them 12th in the table and three points above the relegation zone, thousands of supporters chanted the name of former manager Kenny Dalglish.
They also sarcastically chanted "Hodgson for England" after he replaced David Ngog with Ryan Babel during the second half.
"I am getting used to it, that is the way it is," stated Hodgson, who believes the negativity directed at him has had an impact on his team so he has called for more backing from the terraces.
"We've had to live with that for quite a long time now as ever since I came here the famous Anfield support has not really been there.
"There were the problems with the owners, then Kenny being so popular and not getting the job and it being given to me.
"It is sad and I don't like hearing those things because I am trying to do the best job I can do.
"As manager, you take responsibility for that so I have to take that criticism on the chin as well.
Maybe we are lacking quality and lacking confidence - the negativity doesn't help
"You have seen these players before. They are just not playing like they have done in the past so I think it is time for the fans to really help as well.
"It is not for lack of trying that we are not winning matches.
"Maybe we are lacking quality and lacking confidence - the negativity doesn't help. The players are not getting on the ball for fear of making mistakes."
Liverpool were playing a match for the first time in a fortnight because of postponements and they struggled for any rhythm or fluency.
Striker Fernando Torres continued to look a shadow of his former self, while midfielder Steven Gerrard appeared short of match sharpness on his return from a six-week injury lay-off.
"A lot of our players were below their form and the level we want them to play at," conceded Hodgson. "It was a performance way below what we are capable of and what we wanted to give.
"I'd like to give Wolves credit but I think we were a bit unlucky to lose the game. Probably 0-0 would have been a fair result but it was nowhere near our expectations or hopes.
"It's one of those days that saddens you as a coach and as a player. Tonight the fans go home angry and disappointed because they've seen their team play badly."
Anfield win boosts McCarthy's hopes
However, despite his side's poor form, Hodgson is wary of looking for any quick-fix solutions in the January transfer window.
"It would be dangerous to clear a lot of players out on the basis of one game," he said. "We wanted our renaissance to start today but it hasn't happened.
"Panic would be the wrong thing to do but I'm not the sole arbiter of that."
Wolves manager Mick McCarthy felt his side, who lost to Wigan on Boxing Day but have now moved up one place to 19th in the table, were full value for their win.
"I thought we were the better team and deserved it," he said.
"I think most people's perception of Wolves is that we are going down after being beaten by Wigan and being bottom of the league.
"They probably thought we would come here and sit back and get our backsides slapped and go home with nothing.
"We decided we weren't going to have that and we were going to come here and have a go. I guess fortune favours the brave."
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