The lacklustre performance 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 told Sky Sports.
"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."
Saints duo Gaston Ramirez and Danny Fox were given their marching orders in a fiery clash with the Baggies, which was all the more surprising considering how little both sides had to play for.
"I need to review the images on the TV and we'll see later on if they are actually red cards," he added.
"But what is true is that the team showed a side that has nothing to do with who we are and how we play."