While the Saints were not able to get a result in normal time, as the game ended 1-1, they emerged victorious after penalties.
Lallana, who is hoping his team can avoid relegation from the top flight, was happy with the overall display.
"I thought that we played well," said a pleased Lallana.
"We had a good reaction to conceding a sloppy goal. It’s a bit of a habit for us at the moment, conceding from set pieces. So there’s lots to improve on, but it’s not an easy place to come here. It never has been for me over the years. To walk out of here with a win is good for us, for momentum, for confidence.
"I’ve been there before (going behind early), it’s important to stay calm in those moments, especially when we’re got a lot of young players. But I thought we started the game well and played well. Obviously a blow to concede but still a long way to go in the football match and the it was really encouraging the way we responded to the goal."