Nigel Adkins, who had guided Saints to the top flight from League One in consecutive seasons, was surprisingly sacked by the club's chairman Nicola Cortese in January - despite Southampton being three points clear of the drop zone.
The decision came after a 2-2 draw with Champions League holders Chelsea and many pundits were critical of the move.
However, although Lambert admits he wasn't expecting Adkins to be axed, he told Ben and Kammy former Argentina international Pochettino has had a positive impact at St Mary's, with the club currently seven points clear of the relegation zone in 13th.
"I was shocked when Adkins went because I wasn't expecting him to go," said the striker who has netted 14 times for the South Coast club this term.
"But Mauricio has come in and he's done brilliantly. We've progressed and we're getting better and better."
Lambert revealed the ex-Espanyol boss has made plenty of changes to the way Southampton play and pointed to a high-pressing game and a strictly organised defence as two key introductions from the new manager which have boosted Saints' form.
"We've changed a lot," said Lambert. "The biggest difference is we squeeze high, try to win the ball back early and capitalise.
"That's where most of our success has come from. It came quite naturally, worked straight way and has been getting better and better.
"Also, when we're attacking he gives us freedom to play while he gives us ideas, defensively he tells us how to be and how to set up from their goal-kick."
Although he has had to wait until his 30s for a shot at the Premier League, former Bristol Rovers, Rochdale and Stockport hitman Lambert has flourished in his debut season in the top flight.
And now he's determined to help Southampton - who are virtually assured of avoiding relegation - bounce back from a disappointing 3-0 defeat at home to West Brom on Saturday and finish their campaign on a high.
"It's been a really good season and I've really enjoyed it," said the striker.
"Obviously we've been doing really well of late but as a whole I've absolutely loved it.
"We've got a hard run-in; Tottenham is always a hard place to go and Sunderland sand Stoke are starting to pick up now as well.
"But we've got to rectify Saturday because that will be hurting for a few days - it's horrible when you have a game like that.
"I just can't wait for Saturday to come again now."