Nigel Hasselbaink's put the home side in front before a Stevie May double rounded off the scoring for St Johnstone. Kilmarnock grabbed a consolation through Sean Clohessy but were reduced to nine men after Jackson Irvine and Darren Barr were dismissed.
Wright was happy by the manner in which his side dominated proceedings and emphasised the importance of scoring the first goal of the game.
"After about 10 minutes we were comfortable and switched the ball from side to side," Wright said. "Even if they had 11 men on the park I felt we deserved to win the game.
"I'd be unhappy if one of my players got done the way they were but referees are in an awkward position these days.
"The first goal in the SPFL is vital and you hope that makes them more vulnerable."
A section of the Kilmarnock support vented their frustration at manager Allan Johnston and chairman Michael Johnston during the game.
The Kilmarnock manager said he understood the fans' displeasure and was particularly critical of the manner in which hide conceded the first goal.
"It was really disappointing," he said. "The first goal was really poor and changes the game and to get caught by a long ball over the top was criminal.
"The fans are frustrated and rightly so because we've got to be better than that.
"That isn't good enough and we're all disappointed because we all want to win."