The Gers are in the process of earning promotion from the Scottish Third Division after they were banished from the Scottish Premier League due to financial problems over the summer.
"There is as much pressure on this Rangers team, and the individuals within the team, as there has been on any Rangers team in recent history," McCoist told reporters.
"That's just a fact. It's not an excuse. We all have to handle it. The players have to handle it and the coaches have to handle it too."
Rangers are in Scottish Cup third-round action on Saturday when they welcome Alloa Athletic to Ibrox.