Southampton defender Shaw became the second-youngest player to represent England at a World Cup, behind Michael Owen, in their final Group D game against Costa Rica on Tuesday.
Shaw's long-term future at Southampton has been the subject of intense speculation since the end of the season with Manchester United strongly linked with a move for the full-back.
Asked if he needed to be playing in the Champions League to safeguard his England spot, Shaw said: "You can't really say that because you look at the other teams and they haven't all got Champions League players, have they?
"I don't know. Obviously Champions League would help, playing against world-class players but you can't just say that because you look at other teams that have gone through the groups and they haven't got all Champions League players.
"I don't know. I think we'll have a look at it and just to try and move on in the coming few months."
Shaw also believes England will only get better if younger players are given the chance to play regular first-team football in the Premier League.
"There is only one way that that's going to happen and that is if people are playing week in, week out in the best league in the world," added Shaw.
"I think it has benefited me, the likes of Raheem Sterling and Ross Barkley, so why can't other clubs do that?"