The impressive 2-0 victory over Premier League leaders Chelsea rightly earned huge credit from all quarters.
A third successive league win, and a fourth in all, has boosted confidence within the squad and lifted the team up to ninth in the table - their highest position since the opening weekend of the season.
They have now established a platform for themselves but the next 11 matches over the coming two months are likely to shape their season.
Liverpool travel to Wigan on Wednesday and Stoke on Saturday with the fixture list then giving them games against West Ham, Tottenham, Aston Villa, Newcastle, Fulham, Blackpool, Wolves, Bolton and Blackburn before the home Merseyside derby on January 16.
A good run during that spell will put them in prime position for a top-four finish and so Hodgson is keen for his side to maintain their momentum.
"We have to be very careful. We have to get our feet back on the ground very quickly after the Chelsea victory," said the Liverpool manager.
"There has been a lot of bad things written, false accusations and ludicrous stories being banded around.
"We have got through that by keeping our feet on the ground and trying to ignore it as best as possible and making sure it does not affect our work.
"We now have to make sure any praise does not affect our work. We have to realise we are capable of performances like the one against Chelsea but we are also capable of performances like the one against Blackpool when we were beaten 2-1.
"We have to try to get rid of one of those performances and keep the other.
"But we have four good wins behind us and let's hope we can get at least one win in the next two games as our form away from home has not been good traditionally this year."
One of the players who has had to cope with plenty of criticism over the past two years has been midfielder Lucas Leiva, who was derided on a regular basis during former manager Rafael Benitez's reign.
However, in the last four matches the Brazil international has put in arguably his best performances for the club with yesterday's display against Chelsea the best by far.
Hodgson praised the 23-year-old for the way he has handled the pressure and emerged a better player.
"Lucas has been strong mentally and he needs to be because he is a good footballer, like many of the other players who are getting stick or will get stick," added the Reds boss.
"We don't have that many bad players here but it is a big arena to play in and people expect a lot from players.
"Where Lucas has been strong is to put the criticism he has been receiving over the last couple of years behind him and get out and show he is a very good player.
"I've always believed in him and to be fair my predecessor never doubted him, playing him on a regular basis, so he didn't give the criticism any credence either."
Fernando Torres obviously took all the plaudits after his two goals against Chelsea but Hodgson is seeing signs that other players are starting to finally find their feet.
"A lot of our players need time. Raul Meireles (an £11.5million summer signing) needs time; he is a good footballer but he is not playing anywhere near what he is really capable," said the 63-year-old.
"Maxi Rodriguez had a very good game and Dirk Kuyt came in, we've missed him, and if you are going to single out someone Martin Kelly deserves a lot of praise.
"It was a tough game for him to come into because the left side of Chelsea's attack is a very dangerous one and you have to make some very nuance decisions there and I think he did pretty well.
"He might not have been in the 18 had Sotirios Kyrgiakos and Glen Johnson not gone down with sickness and injury on the morning of the game."