Gareth Southgate's side defied pre-tournament predictions by reaching the semi-finals of the World Cup in Russia, though Saturday's defeat to Belgium in the third-place play-off meant that they missed the chance to record their best tournament performance on foreign soil.
Nevertheless, Ashworth is confident that the future is bright for the 'Three Lions', telling the BBC's sports editor Dan Roan: "I sincerely hope and believe that over the next two, four, six years we've got some players in the system that will help England win.
"I don't think we've achieved anything yet. We have shown some signs of progress.
"But until we win a World Cup or a European Championships, that's when you sit back and say 'OK, we've actually won something'.
"We're a bit young, and we haven't got quite enough caps for a winning team so it is not surprising we didn't get over the line in the end - but it was not a massive surprise to me that we got so far [in Russia].
"We've got some good players in our senior team and some good technical players in our development pathway as well.
"We're probably a little bit short on big-game experience, a bit short on number of national caps and we're a bit young for what a winning national team looks like."
England's campaign in Russia matched their exploits in Italy in 1990, with that and the 1966 World Cup the only other times the 'Three Lions' have reached the semi-finals of the competition.