Lallana was among the goals at St Mary's Stadium as the Saints went fourth in the Premier League.
"He was incredible," Pochettino told Sky Sports News. "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."
The Argentine also reserved praise for 25-year-old Lallana, who he believes is verging on another call-up to the England squad.
"I'm very happy for Adam," the 41-year-old added. "He's a great bloke and a great professional and he's very passionate about 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. His performance has been amazing over the last few games."
Lallana was called up by Roy Hodgson for the match against Ukraine a year ago but did not feature.