The Ayrshire club upset their support by giving Parkhead season-ticket holders - but not their own fans - the chance to buy tickets for the Scottish Premiership game for £20 and reduced concession tickets on Tuesday only.
The initiative also angered Celtic fans who had already purchased full-price tickets at £26.
Kilmarnock responded by offering non-season-ticket holders the chance to claim a free ticket for the upcoming visit of Ross County when they buy a ticket for the Celtic game, while season-ticket holders can receive a £10 gift voucher if they bring a friend to buy a ticket.
Amid reports of potential protests and future boycotts by Killie fans, boss Johnston admits the row has been a distraction but wants supporters to get behind his team who are still looking for the first league win of the season.
He said: "At the end of the day we have to focus on the football, forget about all the stuff that has been going on because the important thing is the football.
"Everybody is forgetting about the game. There is a massive game at the weekend and we need their support.
"We need them to get right behind the team and give them as much encouragement as possible.
"They are Kilmarnock fans at the end of the day and we are playing for the team.
"We want to be successful on the pitch and we need their backing in every game.
"When the fans get behind the players and everybody is pulling in the same direction, it makes a massive difference."
Midfielder David Silva will return to Killie on a short-term deal until the end of the season, subject to international clearance.
The 26-year-old played for the Ayrshire side between 2010 and 2012 before joining Primeira Liga side Olhanense.
Johnston said: "It was a different option. He has a bit of quality going forward and is a bit different from what we have got.
"He has a bit of pace and can go past people so hopefully he will make a difference in the attacking sense."