It is a victory that gives Southampton a seven-point cushion over the drop zone ahead of Sunday's fixtures.
"It was massively important that we got the three points," Lambert said.
"I think we have been unlucky these last few weeks and deserved a few more points than what we've got.
"But I don't really like saying that, I am just happy to say we got the three points.
"You can say all day that you're unlucky and that, but it is the points that matter and we managed to get the points along with a great performance, which is even better."