Saints were 2-1 ahead via goals from Adam Armstrong and Matheus Fernandes before Mohamed Salah struck twice to turn the game around.
Martin said afterwards: "I'm very disappointed but very proud of a lot of the performances. We went toe to toe with the best team in the league at the moment. The two goals are really not good and the penalty is as well. I have a big issue with Adam Armstrong not getting a penalty at 2-1. The goalkeeper collides with him. It's what VAR is there for. I have a big problem with that decision.
"There's a real clear offside as well. There are five of their players clearly offside and the flag doesn't go up. We had a real threat but we should have been better with the ball. I think there's so much more to come. The fight is there, they're running. It gives us a platform to build on.
"It's about work, analyse the problems. It's my fault because we thought we would have a chance on transition play. We have to keep learning and helping the players through it as much as we can. Playing out is what got us to the Premier League and I'm really proud of the players.
"Paul (Onuachu) has been so patient and had to wait for his opportunity. Disappointed to lose him to an injury, hopefully, it's not too bad. Tyler is a really great young player who needs to play at the right place. His ceiling is so high and can play where he wants in the future.
"I think the feeling is very different from the last time this club was in the Premier League. There's no lack of fight. They're really trying."