After a sensational start to the campaign, the Saints had only won once in the top flight since mid-November and their defence had shipped roughly three goals per game in their last four home matches.
But Adam Lallana's second-half strike earning them a deserved victory over the Baggies while returning goalkeeper Artur Boruc kept a clean sheet.
"It's great to get back to winning ways. I'm very happy with the team's performance," Pochettino told reporters after the game. "I think the team fully deserved the win and we had full control of the game."
|5/4||Southampton are 5/4 with Betway to beat Sunderland away in their next Premier League game|
"Regardless of the fact that the team faced some struggles, it's kept on believing. That winning mentality has been recovered."
His West Brom counterpart, Keith Downing, cut a more disappointed figure as he failed to sign off his last game in cartekaer charge with a flourish before making way for incoming boss Pepe Mel.
"We're all disappointed with what we did with the ball and I think we're a little bit frustrated," he conceded. "We restricted Southampton to not many clear-cut opportunities. There were good performances without the ball but we were just a little bit frustrated with the ball."
With the Baggies lacking much in the way of creativity, Mel's introduction as Steve Clarke's long-term successor comes with a promise of high-tempo attractive football, much to Downing's enthusiasm.
"I look forward to working with him next week," said the caretaker. "He wants possession with the ball, playing from the back - aggressive football. It's Spanish football; it's new ideas. It'll be interesting."
Hull City boss Steve Bruce had earlier confirmed contact with West Brom for striker Shane Long but Downing played down talk of a move.
He added of the Irish forward: "I'm not aware of anything. He's under contract and, as far as I know, he'll remain a West Brom player."