The visitors strolled into a 3-0 lead thanks to two goals from Jay Rodriguez and one from Rickie Lambert.
The result piles more pressure on Pochettino's opposite number Malky Mackay but the Argentinian preferred to focus on his side's performance.
Speaking to Sky Sports afterwards, Pochettino said: "I thought we were amazing for the first 25 minutes.
"And, overall, we were excellent. We played really well and it's important to end our recent disappointing run.
"I don't like to single out any player in particular because the whole team played excellent. Hopefully now that will provide us with some confidence.
"It was also vital that we managed to keep a clean sheet because that is not something we have done for a while."
Southampton travel to Goodison Park to play Everton on Sunday after ending a run of six games without a win.