The Baggies had just three wins in 14 league games but returned to form in style, with Marc-Antoine Fortune, Romelu Lukaku and Shane Long all scoring.
The three points saw them set a new club record for Premier League points (48) and wins (14), although it is referee Robert Madley's top-flight debut that stole the show. The Yorkshireman sent off Saints pair Gaston Ramirez and Danny Fox as well as West Brom's Fortune.
Pochettino had not seen the incidents back but could not have missed his side's woeful display. It was the worst since the Argentinian replaced Nigel Adkins at the helm in January and brought an abrupt end to a six-match unbeaten streak.
"From my point of view we just didn't start in the game," Pochettino said. "We didn't really get into the game at all. We didn't feel comfortable, especially when we conceded the first goal in the sixth minute. Then we became a bit fearful of their attacking strikers, who were quite fast, strong and physically fit.
"From that point on we were uncomfortable and never really got into the game. I think we had a bad day but, then again, the good days, the good victories and bad days give me a lot of information as a manager so I have learned a lot from this."
Pochettino was clearly frustrated after the match and knows his side need to learn from the defeat.
Asked if he was more disappointed with the loss or his sent-off players, he said: "I don't know right now. I need to review the images on the TV and we'll see later on if they are actually red cards. But what is true is that the team showed a side that has nothing to do with who we are and how we play."
Fox's red card was particularly frustrating given he was playing in place of injured first-choice left-back Luke Shaw, meaning both will now miss next weekend's trip to Tottenham.
"It is always a problem when one player is injured and another is banned in the same position," Pochettino added. "That represents a problem but Nathaniel Clyne has played there in the past and perhaps he will do again."