Lambert came off the bench to score in their defeat at Manchester City.
He said of his landmark goal: "It means so much.
"You could see how much it meant when I scored because I've been waiting for that moment for a long time now.
"Obviously in the past, I've scored goals at lower level but I was made up to get my first goal here already."
Lambert took heart from Sunday's result as Southampton bid to avoid an immediate return to the npower Championship.
"I thought we looked okay," he said.
"We managed to score two goals, and took the lead, so we're proud of the way that we played.
"We know we've got a hard start this season but we've come here to do well, we've not just come here to survive, and I think we showed that."