Killie are the only team in the Scottish Premiership who are still without a win so far this season and Johnston knows games against County and bottom side Hearts could be crucial over the next couple of weeks.
But, despite the club's current predicament, the stands at Rugby Park are unlikely to be packed out for such an important double-header.
A section of the support have been staging protests against chairman Michael Johnston's running of the Ayrshire outfit, including staying away from home matches.
But boss Johnston wants those who do show up to make their presence felt on the day.
He said: "It makes a massive difference as a player when the fans are behind you and it's positive stuff.
"Hopefully that transmits to the performances on the park.
"One result could change everything.
"Football is all about confidence and, once you start winning games, it completely changes the picture."
Johnston believes the international break came at the right time for Kilmarnock.
"It probably was a good time to regroup and work on some of the things where we have been going wrong," he said.
"Hopefully we can make an improvement this week. The players are all desperate to get a result.
"They have been really bubbly for the last couple of weeks, even when the results haven't gone our way, and they are desperate to make amends."
Johnston previously described the next two games as "cup finals" and his view has not changed.
He said: "Every game between now and the end of the season is going to be massive for us, none more so than the next two games.
"With the situation we have found ourselves in, every game is going to be a big game.
"We know how hard a task it's going to be this weekend.
"Ross County are a physical team, they are always well organised, and we know it's going to be difficult.