The Saints forward, along with Arsenal's Theo Walcott, is the highest-scoring Englishman in the Premier League this season, and notched his 11th goal in his side's 2-2 draw at Wigan Athletic on Saturday.
However the 30-year-old, who has not been contacted by any Three Lions staff about his form, has played down talks that his age is a hindrance to his international career.
"I was disappointed [not to be in the squad]," said Lambert. "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."
England host Brazil in a friendly at Wembley Stadium on Wednesday.