After Szoboszlai had given the visitors the lead, Saints took a 2-1 lead before Mohamed Salah struck twice for the Reds.
"They are a good team, good with the ball," said Szoboszlai. "They scored two quick goals but the most important thing was the reaction. We showed it very well and happy with the three points.
"We had a couple of meetings before the game and we know they build-up from the back. Sometimes they do well, sometimes they make mistakes and that was the case here. We pressed really well and got the goal.
"Everyone knows Mo. He just has to keep going and I hope I play with him for as long as I can."
On going eight points clear as Premier League leaders, he added: "It is a great feeling but it is the beginning of the season. We just need to continue and not think where the other teams are."