The Reds lifted themselves out of the relegation zone after Maxi Rodriguez struck a late winner at the Reebok Stadium to seal a 1-0 win.
And while Hodgson conceded it will still be some time before their revival really takes shape, he believes the club are finally heading in the right direction.
“This is going to be a longer job, it is a rebuilding job,” he said.
“But it is nice that there is a little bit of light at the end of the tunnel and to be able to continue that rebuilding work in a less frenetic atmosphere.
“The players now know they have got the ability to dig in, even in games like this, which is a good thing to know.”
Liverpool host Napoli in the Europa League on Thursday, but before then Hodgson will meet with new owner John W Henry to discuss the future of the club.
And the former Fulham boss is confident that the American is fully committed to taking the club back to the heights it is capable of reaching.
“I have talked with the owner almost on a daily basis because he is very, very interested and committed,” Hodgson said.
“There's a lot of work for him to do to help us but I think he will be happy at least that we have got a group of players who’ve got a lot of fight, spirit determination and a lot of quality.”
A win on Thursday would make it three wins on the trot for the Reds, which would stand them in good stead ahead of next week’s tough Anfield test against champions and league leaders Chelsea.
By Luke Nicholls
