After 120 goalless minutes, John McGinn scored the first from the spot before Scotland keeper David Marshall saved a shot from Eran Zahavi.
Callum McGregor, Scott McTominay and Lawrence Shankland all scored, as did Nir Bitton, Shon Weissman and Abu Fani, leaving substitute Kenny McLean, on for Stephen O’Donnell, to slot his penalty in for a 5-3 win.
Scotland travel to take on Serbia in the final on November 12 where they will look to get through to a finals for the first time since the 1998 World Cup finals in France.
Clarke said: “Yes, it’s a big chance. We spoke about hopefully making a small piece of history for the national team.
“We still have that in front of us. So that was the objective tonight was to make sure that we were in the final next month. And we’ve achieved that.
“I’m really pleased for the players, 120 minutes in a tense, nervy affair and then they had to show a lot of character towards the end to get the win out of the penalty shoot-out.
— Scotland National Team (@ScotlandNT) October 8, 2020
“And thankfully the little bit of work we did on penalties during the week paid off.”
The former Chelsea coach recalled the 2008 Champions League final shoot-out when the Stamford Bridge side lost to Manchester United after being in the position where Blues skipper John Terry had the chance to win it.
He said: “I’ve been on the wrong side of a penalty shoot-out in a big game, a Champions League final.
“We had a penalty to win it and we actually missed it.
“So there was still pressure there as Kenny was walking up.
One down. One to go.
Let's do this. pic.twitter.com/j0b4o9crKU— Scotland National Team (@ScotlandNT) October 8, 2020
“But listen, his penalties during the week were excellent and I had every confidence he would stick it away.”
Israel boss Willi Ruttensteiner said: “It was two organised teams and in the end Scotland were a little bit more lucky because if you watch the first penalty, Ofir Marciano has his hands on the ball, and the second penalty, normally Eran scores.
“He is 100 per cent our best shooter, so I think it was a good play-off game and very sad about the result.”
