Everton midfielder Osman became the third-oldest player to make his England bow since 1954 when the 31-year-old started Wednesday's 4-2 friendly defeat in Sweden.
Britton, 30, admits seeing Osman get the call has only added to his desire to impress Three Lions boss Roy Hodgson and he insists he has not yet given up hope of representing his country.
"The manager [Hodgson] is showing if you are playing well in the Premier League, he will pick you, whether you are Leon Osman at 31 or Raheem Sterling at 17.
"It gives everyone hope out there that it is never too late or it is never too early. If you are playing well week in, week out in the Premier League there are people watching the games and there is always an opportunity."
He added on Talksport: "I'll never give up, I'll try and do well for Swansea and if something comes from that then I'll be absolutely over the moon."