Along with Arsenal forward Theo Walcott, the Saints talisman is the joint-highest English goalscorer in the Premier League, with 11 strikes to his name so far this season.
But, while Walcott is in Hodgson's 23-man party, there is no place for 30-year-old Lambert, despite his impressive form for the Saints on their return to the top flight.
|100/1||Rickie Lambert is 100/1 with BetVictor to be the Premier League's top goalscorer
"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."
Despite an injury to Jermain Defoe and doubts about the fitness of Daniel Sturridge prompting speculation that another striker could be added to the England squad, Lambert insists that his focus remains on ensuring that Southampton retain their Premier League status.
"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," he remarked.
"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."