A second-half strike from Rory McKenzie secured a 1-0 passage to the third round on Tuesday night, as Killie again claimed the Ayrshire bragging rights.
The last time they defeated Ayr was in 2012 in the semi-finals en route to claiming the trophy.
Johnston said: "Hopefully it's a good omen. You could see how much it meant to the players. It's massive.
"You could see the support we had. It was fantastic and they got right behind the team.
"To be fair so did the Ayr supporters and it was a good atmosphere to play in. It's about getting results and we are delighted to be in the next round."
Johnston was understandably keen to single out match winner McKenzie for praise.
He said: "It was a great finish. We know he's capable of that, he's a real goal threat.
"We are delighted for him to get a goal as he has been unfortunate in the other games so far this season."
He added: "In the first half we didn't pass the ball as well as we have been.
"It was maybe nerves as it was the first derby for a lot of the boys but we were better in the second half.
"We controlled the game, passed the ball well and we were unlucky not to score on a few occasions."
Ayr boss Mark Roberts had no complaints about the efforts of his own players.
He said: "The boys did fine. I thought they really competed in the first half and there wasn't a lot between the teams.
"We felt that Kilmarnock were there for the taking but in the second half they put pressure on us.
"Kilmarnock were probably deserved winners but I'm proud of the boys."