The Croatia defender, signed from Lyon in the summer, partnered Jose Fonte in the middle of the Saints defence and was able to celebrate a clean sheet as well as the victory earned by Rickie Lambert's late penalty.
Southampton sold out their ticket allocation at The Hawthorns and Lovren was full of praise for their support, which he felt was a big help in the team's efforts on the pitch.
"The atmosphere and the fans were amazing," Lovren told the club's official website.
"They were behind us for 90 minutes and they were like a 12th player. They were unbelievable, and it's because of them that we won the game.
"I'm very proud of the team because we've made a very good start and got three points. It was not easy, but this is the Premier League. It's fantastic to play here.
"In the morning we didn't know who would play but I told my team-mates and the coach that, whether it's the right or the left, it's not a problem for me so I am ready for the team, and I will give my best.
"In the end, we were pretty good defensively, and that's everybody - not just the four in the back line. It was unbelievable."