The England striker had not found the net since striking from the penalty spot at West Bromwich Albion on the opening day of the season.
But he was back among the goals earlier today with a superb free-kick that followed up Dani Osvaldo's first for the club to see off newly-promoted Palace.
"I'm over-the-moon to get on the scoresheet because I haven't scored in a few games," Lambert told Saints Player
after the game.
"I didn't need people to let me know I haven't scored because I know that myself. To go one or two games is frustrating, and four is obviously more so.
"I was desperate to get on the scoresheet sooner rather than later, so I'm happy it came today.
"For it to come from a free-kick is a bit of a surprise because my free-kicks in training haven't been going well at all.
"We didn't panic like a lot of teams might have if they couldn't break a team down," he continued.
"We knew that, if we kept on going, doing our thing and quickened our passing around the box, we would get a chance and one would go in sooner or later – and it did.
"Dani did terrifically for his goal – he's hit it, got it on target and it's gone in the back of the net.
"That's what happens when you take your chances, and that'll obviously give him the confidence he needs – and it gave the team confidence to go on and get another goal."
Today's win – Saints' first in the league at St Mary's this season – leaves the side flying high in fourth place with 11 points from five games, something that Lambert is determined to build upon.
"We've been desperate to get a win in front of our fans, so to get it today after the result against Liverpool is brilliant," he affirmed.
"We've been strong at home over the last few years but we hadn't managed to get a win here [this season]. We're off the mark now, so we're buzzing.
"A good start is important to any team in any season, but just because we've done well doesn't necessarily mean we can lay off a little bit.
"We'll be trying to improve because we know the teams around us in the league are going to pick up points so it's going to get harder to stay where we are, but we're confident we can do it.
"It's very nice [to be fourth], so let's try to stay there now. It's early doors, so we've got to take our start into the rest of the season and push on so we can stay there."