Lambert has adjusted to Premier League football superbly after spending most of his career in the lower leagues and his 11 goals make him the joint-leading English scorer in the division with Arsenal's Theo Walcott.
The 30-year-old revealed he has not been contacted by any of the England staff despite his form, which continued with a goal at Wigan on Saturday, and he said: "I was disappointed (not to be in the squad).
"I'm not saying I was expecting it but I was hoping, and it wasn't to be. But hopefully I can show until the end of the season that I am good enough, not just that I deserve a chance but that I am good enough.
"If it comes, it comes and if it doesn't, it doesn't. I'm just going to try to help Southampton, try to score goals and push Southampton up the league table.
"I'm not going to focus on the England squad too much but I am hoping I can get a chance.
"I don't think my age is a hindrance. I've just got to try to prove to them that I'm good enough. I've got quite a lot of games left to do that."