Adkins' side found themselves 2-1 down with five minutes to go but Lambert levelled when he was brought down in the box before snatching the winner in the 88th minute after an Alan Dunne handball.
It was a fourth hat-trick of the season for Lambert who now has 28 for the campaign and it kept in-form Reading at bay, two points adrift, in the race for the npower Championship top spot. Adkins said: "I still believed we would win with seven minutes to go."
He added: "We've got goalscorers in the team, we were on the front foot and you've just got to believe a little bit. We knew before the game it was going to be very challenging, it's always a tough place to come to. I thought we started the game well, moved the ball around well and justifiably went in front. It was a super goal.
"The first one is a clear penalty, where Rickie is brought down, so there can be no qualms about that. Then the corner comes in, the referee (Fred Graham) is in a perfect position, with nobody blocking his view. Two players go up for the ball, one a Southampton player and two, (including) Dunne, from Millwall.
"It looks from the video that either of them, but more likely Dunne, actually handles the football."
Lambert put the Saints ahead in the 16th minute after a fine pass from Morgan Schneiderlin but Millwall hit back when Jose Fonte put through his own net six minutes later.
Paul Robinson's screamer in the 28th minute handed the Lions a lead they kept until 85 minutes, only for the Saints to capitalise on two spot-kicks, leaving Millwall boss Kenny Jackett feeling hard done by.
"I felt for them to get both decisions, was harsh on us," said Jackett. "I haven't seen either one again, but to get both of those away from home is somewhat fortunate. It was a terrific performance, to come back from a goal down and not the brightest of starts. For us to get nothing out of that game is ultimately very frustrating.
"It's a massive game and we can't dwell on this now. Whether it was good, bad or indifferent, we can't be too disappointed that it affects the rest of our week. The atmosphere in the dressing room is very subdued, very angry but we've got to get over this very quickly. There can't be any hangover whatsoever."