Lambert has shone on his first season as a Premier League player, netting 11 goals in 25 matches.
The 30-year-old's haul is the highest by an English player and led one bookmaker to offers odds of 3/1 on him receiving a first call-up for Wednesday night's match against Brazil.
In the end, England boss Roy Hodgson overlooked the striker, something Pochettino was relieved about after left-back Luke Shaw picked up a knock on England Under-21 duty.
"For me, they are all worthy of playing for their national teams," Pochettino said of his new charges.
"[But] it would be better for Southampton that they are not with their national teams after what happened to Luke Shaw.
"It's natural they should have enthusiasm to play for national team, but they have to be calm and everything comes bit by bit over time."
Shaw picked up a ligament issue ahead of his Young Lions debut against Sweden and is a doubt for Saturday's late kick-off against Manchester City.
Fellow full-back Nathaniel Clyne, another that dropped out of the Under-21 squad, may also be unavailable, with Gaston Ramirez and Guly do Prado also possibly out.
"We have several players recovering from situations that have happened to them over the last couple of games," said Pochettino, who will almost certainly be without centre-back Jose Fonte.
"I can't confirm at the present time whether they will be ready for Saturday or not.
"I hope they will be available for the game. Luke Shaw has come back with a problem after his time with the England Under-21s team.
"We don't know if Adam Lallana will be ready right from the start. He is recovering from injury so we don't know yet."
Should the winger make his first start since December 8, it would be a huge big boost to Pochettino, who has yet to secure his first win since replacing Nigel Adkins at the St Mary's helm.
The Argentinian knows it will be tough to secure his first three points against City, highlighting David Silva, Carlos Tevez and Sergio Aguero as the key threats.
"It's obvious that those two players plus Silva are great players," Pochettino said.
"We know that we have to stop the players getting balls to these three players.
"We know any of these three can decide the match at any time so we have to stop the ball getting to them."
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