The 0-0 draw in Cardiff means Wales must wait before confirming their place in France.
The team remains top of Group B but will have to wait until next month to seal their spot after second-placed Belgium beat Cyprus.
It would be Wales' first appearance at a major tournament since the World Cup in 1958.
Belgium won 1-0 in Cyprus in the game which kicked-off later, at 19:45 BST.
Chris Coleman's side only need one point from their remaining two matches.
They play Bosnia-Herzegovina away on 10 October and Andorra at home on 13 October.
"It's a shame for the supporters we didn't do it by beating Israel, but it is coming for us," said Coleman.
Prior to Wales' game at the Cardiff City Stadium, some fans complained about missing kick-off, with posts on Twitter suggesting hundreds had to queue outside the Cardiff City Stadium.
Mark Ludlam tweeted from @basementjack: "Stewards blaming fans for only giving themselves 30 mins to get in to CCFC Stadium. How long should it take?"
Celebrations are on ice after a draw against Israel left Wales agonisingly close to qualifying for Euro 2016.