The striker has been in a rich vein of goalscoring form on the road in recent weeks, but went into today's match having not found the net at home since the draw with Norwich in late November.
But, after scoring Saints' second in today's 3-1 victory with deflected free-kick just after the half-hour, 13-goal Lambert went home happy.
"The lads are buzzing – it was a great performance from the boys," he said at full time.
"I don't like saying it because you normally get what you deserve, but we have been unlucky in the past few weeks not to get three points somewhere – but we got exactly what we deserved today. It was a great game and a great result.
"Today we got that little bit of luck, and the result is absolutely what we deserved from the performances we've been putting in."
Saints got off to a dream start after just six minutes, when Morgan Schneiderlin swept in Jay Rodriguez's nod-down for his fifth goal of the season.
"The first goal is massively-important," said Lambert. "It was a calm finish by him (Schneiderlin) again, and he has been absolutely superb this season.
"As soon as that went in, the fans got right behind us and we went from strength to strength."
After a number of near-misses, Saints' second arrived on 33 minutes when Lambert's 30-yard free-kick deflected off the Liverpool wall and beyond goalkeeper Brad Jones.
"It wasn't my best-struck free-kick," he admitted. "I've hit some decent ones this season, but we got a little bit of luck today – and we deserved that. We haven't had much luck, so we'll take that.
"We were unlucky not to be more goals up but before that but that two-goal lead gave us a bit of a margin, which we definitely deserved."
But, after a dominant first-half performance, Saints were pegged back on the stroke of half time when Philippe Coutinho – who played under gaffer Mauricio Pochettino at his former club Espanyol – stole in to poke past Artur Boruc.
"We were unlucky to go in at half time only two-one up," said Lambert. "They had chances, but the chances we had were clear-cut and we should have done better – especially me.
"We were disappointed to concede right on half time. It was frustrating because that's the worst time to concede a goal because it lifted them, but we got ourselves together at half time.
"We were confident that we could go out in the second half and go again with the high tempo and with the pressure that we did.
"We were terrific again in the second half. We didn't have as many chances as we did in the first half, but we limited them to very few."
Jay Rodriguez's goal ten minutes from time rounded off the victory over the club Lambert grew up supporting, leaving him pleased with what it will do for his side's Premier League standing.
Saints rose to 15th and seven points clear of the drop zone, but the striker insisted that he and his teammates must remained focused.
"Obviously, it means a lot to play against Liverpool but the main aim was to get three points today," said Lambert.
"I've managed to score a goal to help my team win, and that's the only thing I was thinking of.
"This result is very important, but we do know that some teams below us have games in hand," he added.
"We've just got to keep on going and picking up points, so we've got to concentrate on our next game now.
"The gaffer hasn't mentioned any points targets, so we're just looking to pick them up in every game."
Because of international fixtures, Saints must now wait a fortnight until their next game – the visit of Chelsea to St Mary's.
And Lambert admitted that, given the impressive nature of today's win, he wished he and his teammates could get back onto the field sooner.
"That's one thing that I haven't enjoyed in the Premier League," he said of the fixture schedule. "I'm used to playing Saturday-Tuesday-Saturday-Tuesday, which I like.
"It's frustrating when you have to wait a few weeks, but I am thoroughly enjoying this season.
"This was another terrific win by the boys, and I couldn't have asked for any more."