The Bairns are now in the relegation play-off spot, level on points with the Wasps who have a game in hand.
After the game, McKinnon said: "Their goalkeeper has had five excellent saves, when we score we have a great chance after but we just couldn't put the ball in the net.
"We get caught with a sucker punch at the end and it's a really frustrating day for us. It was an opportunity missed.
"It's all to play for, there are still five teams bang in it, so we just need to regroup and go again."