Lambert himself was to blame for missing two good chances in a forgettable 0-0 draw with Everton at St Mary's on Monday night.
And the striker was annoyed after a recent run of good form under former Southampton boss Nigel Adkins, who was sacked last Friday and succeeded by Pochettino.
"It was a good point but it's disappointing not to get all three," Lambert told Sky Sports.
"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."
Meanwhile, midfielder Morgan Schneiderlin admitted Southampton still did not know much about Pochettino.
But they will now go to Barcelona on a training camp where that can change.
"I think he's been great," he said. "In the next couple of weeks we will get to know him better. Now we go away for a couple of days to get to know him and what he really wants from us."