Iceland earned European qualification for the first time after a 0-0 draw with Kazakhstan in Reykjavík on Sunday.
Meanwhile, Wales must wait to join the party at Euro 2016 next summer.
Chris Coleman's side knew three points against Israel in Cardiff would see them qualify for a major tournament for the first time since the 1958 World Cup.
But despite dominating throughout they were held to a 0-0 draw by stubborn opponents who remain in the hunt for qualification in Group B but showed no attacking intent at all.
They missed an early chance to take the lead when Aaron Ramsey headed over from close range after Andy King's shot, following a pass by defender Jazz Richards, had been stopped by Ofir Martziano.