The Saints returned to action following their disappointing penalties loss to FC Minsk in Europa League qualifying on Thursday and managed to hold Killie goalless to pick up a valuable point which was welcomed by Wright.
"I'm delighted with the point,” he said.
"It was an excellent point for us, particularly after the emotion of Thursday night and the physical exertions, even though we did freshen it up a little bit.
"I'm really pleased and I thought we showed a lot of character.
"(Killie boss) Allan (Johnston) probably thinks they deserved all three points but, with the effort we put in, I thought we deserved to take a point from the game."
St Johnstone find themselves fourth on the SPL table following their opening weekend 1-0 win over Hearts and Sunday’s draw with Killie.