Kane slipped the ball under keeper Scott Brown in the 70th minute to earn Saints a 1-0 victory over Aberdeen.
With Dundee United winning comfortably in the Tayside derby, St Johnstone needed the goal to keep alive their Europa League chances and Wright said: “We just told him to play as high up the pitch as possible and hopefully he would get a chance but to get it so quickly.
“He has done well but he hasn’t scored a goal and it’s a big finish for him because he has got a wee bit of time to think about it. It was a great first touch and I’m really pleased for him. It’s a big goal for us.
“It was difficult because we knew what was happening down at Tannadice and knew we had to win the game. But we knew if we kept it 0-0 long enough and got Faddy on, and Brian Graham and Kano, we could sneak something. All three have done well as did the 11 that started the game.
“It showed good mental strength knowing we had to win the game.”
Saints will achieve a fourth consecutive Europa League qualification if Inverness beat Falkirk in the final of the Scottish Cup next Saturday.
Wright added: “It’s a remarkable achievement finishing fourth. The icing on the cake would be Europe.”
Aberdeen had hoped to give skipper Russell Anderson a winning send-off but it did not happen and manager Derek McInnes said: “Jim served the club so well over a period of time. Some decisions are harder than others as a manager and that was particularly tough.
“But any decision I make on anybody’s future is always based on what is best for the club. I told Jim a couple of days ago to give him the opportunity to have a farewell to supporters knowing it was his last game but Jim refused that, which we fully respect.
“We wish Jim well and I have a lot of respect for Jim but the decision was totally football. People move on and changes have to be made at times.”