Pochettino's men had started the Premier League game in a positive manner at the St Mary's Stadium, with Adam Lallana's well-placed shot beating Hugo Lloris to give Southampton a 13th-minute lead.
Emmanuel Adebayor stretched to reach Roberto Soldado's cross and level proceedings 10 minutes before half-time before a goal glut after the break. An own goal from Jos Hooiveld and Adebayor's curled left-foot effort sandwiched Rickie Lambert's tap-in, with all three goals coming in the space of 10 second-half minutes.
Pochettino praised the manner in which Southampton performed in the opening exchanges, but conceded it was difficult to stay in the game once Tottenham had found an equaliser through Adebayor.
"(It was) very frustrating, I am very angry about the result," he said. "We actually dressed up as Santa Claus and gifted them so many chances.
"We started very well in the first half, we went ahead 1-0 and nearly got the second goal.
"But then we conceded the equaliser, it was hard to get back into the game especially in the second half."
Lallana was a bright spark for Southampton, scoring the team's first and laying on the second for Lambert.
And Pochettino thought the England international was unlucky to finish on the losing side.
He added: "I would change Lallana's great performance for a positive result. It would be nice to have the positive result to go with his impressive performance.
"When you talk about individual performances, it's great he played well and all credit to him but it's overshadowed by the fact we weren't able to get a win."
The defeat means Southampton have won only one of their last eight Premier League fixtures and sit ninth ahead of Thursday's visit to Cardiff City.
