The draw means that the Saints are now four points clear of the relegation zone, but Lambert believes that his side could have taken more from the match.
"It was a good point but it's disappointing not to get all three," Lambert told Sky Sports News. "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."
Lambert has scored 10 Premier League goals so far this season, which is more than any other Englishman.