The Argentinian struck four minutes from time to settle a keenly-contested encounter at the Reebok Stadium 1-0.
Related ArticlesBolton 0 Liverpool 1Premier League tablePremier League actionBolton Wanderers v Liverpool: as it happened.Premier League fixturesTelegraph player raterThe goal catapulted Liverpool from 18th to a more respectable-looking 12th position ahead of next week's tough Anfield test against champions and league leaders Chelsea.
Hodgson said: "It is still too early to be too optimistic but at least it is a step in the right direction.
"The players now know they have got the ability to dig in, even in games like this, which is a good thing to know.
"It is nice to see a little bit of light at the end of the tunnel."
Hodgson's caution was understandable after his side struggled to overcome a determined Bolton.
The visitors started well, with Fernando Torres missing two early chances, but there was little to choose between the teams thereafter.
Sotirios Krygiakos had two good headed chances, Steven Gerrard drove wide and Rodriguez narrowly missed with an overhead kick for Hodgson's men.
For Bolton, Stuart Holden volleyed well at Jose Reina, Kevin Davies and Zat Knight went close with headers and Johan Elmander shot wide.
The hosts also had three penalty appeals of varying strengths turned down.
"We had so much of the ball, so many situations where I thought we had opportunities and we wasted them," said Hodgson.
"Luckily one more came up and we took it.
"When you don't do that you are always worried one of the long throws or long balls into the penalty area is going to bounce kindly for the opposition and you are going to lose the game.
"I was delighted that didn't happen. I thought it was a very gritty performance from our back four."
The only downside for Liverpool was the loss of Joe Cole with a hamstring injury which could force him to miss the visit of former club Chelsea.
Defeat was harsh on Bolton, who had looked set to claim at least their seventh draw of the season, but manager Owen Coyle expects his team to respond.
Coyle said: "I felt it was cruel on the team given the efforts they put in. We dominated the game for large periods.
"The application and endeavour the players are showing is there for everyone to see and the only disappointment is losing the game.
"We will take our medicine, our kick in the teeth, and look to bounce back quickly."