Shiels had not produced a win since March 19 last season and admitted it was nice to be back on the winners board after 10 matches without maximum points.
"I don't think we have anything to prove to anyone," Shiels said. "One of the greatest qualities a person can have is persistence.
"We had a tough run-in with a weakened team but we persisted to make mistakes and tried to produce from that.
"The greatest feeling for me today is we made a mistake for the goal from trying to play out, but the players had the courage to take the ball everywhere on the pitch.
"The critics will say 'how can we try to play out when we conceded the equaliser?' But our first goal was a result of us playing the ball out from the back.
"I say to the players 'be brave, take the ball, play out, it doesn't matter who it's against, because that's our way'."
Killie got the points thanks to two goals from Paul Heffernan (3rd and 71st minutes) which bookended Garry O'Connor's leveler in the 14th minute, Paul Hanlon's own goal just before half-time and James Dayton's brilliant 25-yard free-kick in the 65th minute.