Coleman's future was called into question on Tuesday night following Wales's 3-0 defeat to Serbia in World Cup qualifying - a result that has left the side at the bottom of Group A.
"You have to back him," BBC Sport quotes Rush as saying. "In the modern game, people can be guilty of looking for instant success, and success sometimes does not happen.
"But who is going to do it instead of Chris, if they want someone Welsh in charge? Give him another two years and see what he can do. It starts from now, if we are serious about doing something for Euro 2016."
Coleman, who won 32 caps as a player for Wales, took charge of the team in January 2012.