Despite a host of chances for the home side, Peter Odemwingie's 75th minute strike earned the Baggies an unlikely win.
"I can't deny that we rode our luck and Liverpool played very well and put us under pressure but it was a fantastic rearguard action," said Hodgson.
"It was nice that at this stage of the season we have the fight in us to hang on to the result.
"We weren't without our own efforts but on the balance of the game they had so many chances that they must be disappointed they came away with nothing."
The win has lifted West Brom up to 10th in the Premier League table, while Liverpool have slipped down to eighth.