Richie Foran took advantage of some lax defending to head home an early opener but Kilmarnock came out in determined fashion after the break to level within five minutes, although there was a touch of fortune about their goal as Graeme Shinnie's clearance bounced off Barry Nicholson and in.
Johnston said: "The first half we did all right at times but the second half I thought we came out and played really well, and lost a really soft goal after getting ourselves into a strong position.
"I sound like a broken record, but we can't afford to lose goals as easily as that. The first one is from a throw-in and all it is is the second ball. And the second one is just a long ball over the top and we have to deal with it better.
"You have got to learn, you can't keep on making the same mistakes because you can't afford to (need) two and three goals to win a game of football.
"The boys know the mistakes they are making, we have shown them and been over them in training."
Johnston, who started with Jeroen Tesselaar and Jackson Irvine in central defence, added: "Darren Barr's wife is in labour and he had been at the hospital all night so someone like that is obviously a big miss as well."