Wilmots pleased with Belgium's response
Marouane Fellaini opened the scoring in the ninth minute in Jerusalem but the visitors were forced to do it the hard way following Kompany's sending off.
Kompany saw red for a second bookable offence with 26 minutes remaining, though Belgium held on to go top of Group B.
"I couldn't see why Vincent Kompany got the second yellow card but as a [former] player I have great respect for him," Wilmots said afterwards.
"Everyone continued to work and did most back for the score. The players responded well, the team was very supportive."
Tuesday's victory helped Belgium move top of the group, ahead of Wales on goal difference after five matches.
Israel - unbeaten before the international break - are two points adrift following back-to-back defeats.
"It is hard for Israel after starting the campaign with nine points out of nine and then losing two home games," Wilmots added.
"It must be hard but we came ready to win the game and I believe that it wasn't luck why we won."
Opposing coach Eli Guttman felt Israel deserved to take something from the match, praising his players for a "dynamic" performance.
"We didn't deserve to lose this match – one moment of lost concentration and the whole game went," said Guttman.
"This was the Israeli team I wanted to see, dynamic and eager.
"We started slowly but we upped the tempo. The goal we conceded angers me because we had markers on all the players, yet we lost focus and that hurts.
"I'm going home tonight a different man than after the game against Wales. We played against a team rated fourth in the world and we pushed them hard. I want to thank our wonderful crowd. The match against Bosnia is now crucial and we hope to push on and finish second in the group."