Mauricio Pochettino's side went into the game on the back of a run which had seen them win only one of their last nine Premier League matches but Lallana's 66th-minute strike secured a welcome three points.
The England international dispatched Gaston Ramirez's pass and celebrated by revealing a T-shirt which wished his mother a happy birthday.
Lallana told Sky Sports News: "The most important thing was getting the three points.
"We have had a tough run of late but we have had a great week, a great build-up to the game, and it was great to implement that.
"We worked hard, we had a lot of possession, so we knew we had to be patient and it paid dividends in the end. We got the goal and kept the clean sheet which was the main thing.
"I think West Brom came here to try and make it difficult for us and maybe would have been just happy with a point. So we knew we just had to keep knocking at the door and eventually one of the half-chances if we could just take it - and we did."
Lallana believes Saints can now build on this win after emerging from a tough run of matches over the last few weeks.
He added: "We have played a lot of the top teams and I think they showed us a lot of respect by being right up for the games.
"But we knew we just maybe had to get back to basics and it was good having the whole week to prepare for the game, maybe mentally, and it was fantastic for us getting these three points.
"It's good that we are getting a few key players back fit now and we can give it a right good push at the back end of the season."