Any chance of a happy 40th celebration for the Killie boss went by the wayside when Gabriel Reuben was sent off on 22 minutes having been booked twice in quick succession.
It took until the hour mark for United to find a way through, but three more goals followed before Kris Boyd's late reply, and the visitors have now won five on the spin.
Johnston said: "It was always going to be a hard game against a confident United but I didn't think there was much in the game before the sending-off.
"The first booking was harsh and I think perhaps the referee was too keen to get his cards out. I can't complain about Gabriel's second booking but going down to 10 men is frustrating and spoils the game for everyone.
"I asked the ref (Euan Norris) about the double booking and also at 1-0 when the ball hit a United player's hand. He said it was unintentional, but both of them were big decisions."
United have now scored 21 times in five games, and boss Jackie McNamara said: "The players haven't spoken about scoring four goals in games recently, they are just interested in keeping going to the final whistle.
"We are always confident of scoring, whether in the first minute or the last and even when the subs come on the are keen to get involved and grab a goal.
"The elements made it difficult and we told the players at half-time to keep playing football and moving the ball quicker as the play was condensed in the first half.
"Obviously that led to a lot of bookings but I don't think Kilmarnock can have any complaints as we have turned their players and the referee was been spot, including the red card as Stuart Armstrong was twice getting away from his opponent."