Saints emerged 2-0 winners from a pulsating, end-to-end encounter at St Mary's, despite spending most of the match on the back foot.
The Swans dominated the majority of play but fell to strikes from captain Lallana and substitute Jay Rodriguez as Saints secured a third successive league triumph.
Southampton also picked up a fifth clean sheet of the season, with goalkeeper Boruc pulling off a string of fine saves to keep the visitors at bay.
"He was incredible," Southampton boss Pochettino said of the Poland international. "He did ever so well, but it just shows we have full trust in his performances and his skill, and also in our other keepers.
"We were able to keep another clean sheet, which was a massive positive for us, but Boruc has our full trust to be our number one keeper.
"I don't know what happened in the past, but in the eight months I've been here he's been excellent for us.
"There's great competition between the three main goalkeepers and behind in the youth teams, so we're very happy with the great atmosphere between them."
While Boruc was Southampton's best defensive player, goalscorer Lallana shone going forward.
After taking a while to adapt life in the top flight, the 25-year-old has impressed for Saints this term, leading to suggestions he could follow Rickie Lambert into the England set-up.
"I'm very happy for Adam," Pochettino said of Lallana, who was called up for England's World Cup qualifier with Ukraine in September 2012 but did not play.
"He's a great bloke and a great professional and he's very passionate about this club, about Southampton, so I'm happy for him.
"I'm very happy that he scored and for everything he represents - all the good values at this club.
"It's not my decision in the end, but if he keeps performing as he did today he'll be actually very close to getting that call up to the national side.
"I don't like to talk about what I've done in his game. It's an overall group of people who are helping to make this club better.
"I want to thank him for his kind words about, but there's a structure at this club to help everyone improve and that goes from the chairman to the cleaning lady.
"The one person who deserves all the praise for his improvement is the player himself. His performance has been amazing over the last few games."
Swansea counterpart Michael Laudrup, meanwhile, was left ruing missed opportunities after seeing his side fail to follow up Thursday's Europa League win against St Gallen with another positive result.
Michu and Wilfried Bony were denied by fine Boruc saves, while Saints academy graduate Nathan Dyer hit the inside of the post before half-time.
"I don't know if frustration's the right word, but I think there are always positives and negatives in every game," the Swans boss said.
"Before we started this season, we said it would be difficult for the team and we've seen a lot of cases around Europe of teams who have to play on Sundays.
"I can only say we are doing well, and are playing well in all the games after midweeks.
"Today was the seventh game in 20 games. I thought it could be some players tired. You play every three days, but I really didn't see that.
"It's true Southampton were the best team in the first 10 minutes, but since the goal I think we dominated the whole game.
"The second half we dominated form the first to last minute, but maybe not creating the same number of chances."