A young Rangers side were booed off the park following a goalless home draw with Stirling on Saturday after failing to impose themselves on the game.
Rangers have won only two of their last five Irn-Bru Third Division games, although they could clinch the title on Saturday after facing Montrose at Links Park.
Durrant told Rangers TV: "These are difficult times but we've just got to get on with it. It's the players' jobs to win games and entertain people.
"In the last few weeks, we've seen the fans' frustrations because we've not done that and pressure is part and parcel of playing for one of the Glasgow clubs.
"There's a winning mentality here and that has to be installed into the players right away. You either come in and be a winner or someone else comes in and is a winner in your place.
"It's that simple. It's quite a ruthless situation but you've got to step up to the plate week in, week out. The fans demand that and there will be nerves, but collectively we've all got to rise above that and deal with it."
Durrant, who was a Rangers regular aged 18 and scored on his Old Firm debut, added: "If you want to play for Rangers and you can't handle the pressure when we're in the Third Division, it doesn't bode well for the future.
"We can see the finishing line and I don't know if the players are so far in front that they've just taken their foot off the gas a bit. But we had a meeting yesterday, we've addressed the problems we've got and our aim is to go on and win the league before we start enjoying ourselves."
Rangers will have Ian Black available after suspension at Montrose but they are still expected to be without the injured Darren Cole, Lewis MacLeod, Dean Shiels and Andy Little while Ross Perry and David Templeton are unlikely to make their comebacks on the artificial surface. Francisco Sandaza remains suspended by the club.