The Ibrox club is in turmoil following their 4-0 William Hill Scottish Cup semi-final defeat by Celtic at Hampden Park which ultimately led to the suspension of club captain Lee Wallace and veteran striker Kenny Miller.
Neither played in the game on Sunday but they were both called to a disciplinary meeting at Ibrox on Tuesday morning amid claims they undermined manager Graeme Murty in the dressing room afterwards.
Rangers have still to travel to Celtic Park on Ladbrokes Premiership duty but the former Gers midfielder, who played for the Govan club between 2007 and 2015, believes they have to first get back on track against the Jambos and look to secure second place in the table.
Speaking at Ayr racecourse ahead of the Coral Scottish Grand National on Saturday, McCulloch said: “Probably the first 20 minutes of that game will be the most important of the run-in.
“They need to start really well, get the fans behind them and just go and win the game.
“There is no place for excuses now.
“Hearts’ game plan will be to start well and try to get the fans to show their frustration against the team, like any team going to Ibrox.
“It is up to the Rangers players to show how much it means to play for the club.
“I am pretty positive they will be hurting from the Old Firm game.
“It is a good chance to finish second and get that European place in the bag. There is still a chance to salvage something from the season.”
Celtic are one win away from clinching a seventh successive title and are on course for an historic second successive domestic treble.
The former Kilmarnock boss believes Rangers can close the gap - but admits to being uncertain as to the timescale.
He said: “It is not a magic wand. There needs to be some players going, some fresh ones brought in and that costs money so there needs to be investment in the team.
“It can be done. You have to believe it can be done. How long that will take I don’t know.”