Returning to the World Cup after 64 years, Wales ended the tournament on one point, finishing bottom of Group B following a 1-1 draw with the United States in their opening game and a disappointing 2-0 defeat by Iran in the second match.
Bale was anonymous in attack in the first half against England before coach Rob Page had to substitute him at the break due to a hamstring issue.
"I'll keep going as long as I can and as long as I'm wanted," Bale, Wales' most-capped player, told the BBC.
"It's a difficult moment now obviously but we go again.
"We have a (European Championship) qualifying campaign starting now again in March and we have a few months to get away from international football now which is obviously disappointing, we'd love to stay longer."
Page said Bale gave an "excellent" performance before the break.
"Bale is fine and he wants the best for the team," Page told reporters. "He knew if he went back on the field he would have been around 70% (fit). When you play against a team like England, you can't carry anybody.
"He put in a big shift ... I don't think it will be the last time you see him in a Wales jersey."
Despite the defeat at the Ahmad bin Ali Stadium, Page was proud of the team, who reached the World Cup via the play-offs after overcoming Austria and Ukraine.
"We look back with frustration but it's an amazing achievement for the players to get here in the first place. We build on that, that's the bigger picture," Page said.
"We are just disappointed because we know, in a couple of games, we haven't really shown our true colours and that's really the most frustrating. We want to learn from it."
