The Saints and Toffees drew 0-0 at St Mary's Stadium in manager Mauricio Pochettino's first game in charge since last week's sacking of Nigel Adkins but the skipper believed a win was in order after a fairly solid performance and a few missed opportunities from himself.
"It was a good point but it's disappointing not to get all three," Lambert told Sky Sports 1.
"Especially in the first half we played some really good football and I should have put at least one, maybe two away.
"I'm disappointed not to put one in the back of the net but we played well defensively and that's positive.
"Everything I've seemed to touch has gone in lately, but today it wasn't to be. I was still hoping to get a chance in the second half but it didn't come."