The Scottish giants suffered a shock 1-0 defeat to Stirling Albion at the weekend as their results away from home in Division Three continue to cause significant concern
Stirling were the bottom side in the Scottish Football League before Saturday’s game, but they managed to pull off a famous 1-0 victory over the Gers at Forthbank Stadium.
That means Rangers have picked up just three draws and one defeat from four away matches in Division Three so far this season, leaving them third in the table.
McCoist told reporters: "I just feel frustrated. That's my over-riding feeling - frustration at not getting away victories in the division.
"At the same time, there is a determination to get it right and put it right and we will.
"We've lost a league game here. We always knew it would be a lot harder than a lot of people were making out and it's certainly turning out that way.
"But we've got a league that we should be winning and at this moment in time our away performances are posing us a big problem.
"We will work hard and strive to turn the corner and we will. I'll make sure we will."
McCoist says he understands if his position is now put under increased scrutiny given the side's sub-standard start to the new campaign.
"Nobody needs to remind me of what's required from any football manager and that is results," he added.
"We have lost a league game that we are really sore about but we will bounce back.
"Time will tell if we are good enough to get out of the division - I would stand here and tell you we are and we will be.
"That's my belief and nothing has changed, but saying it is one thing, we will have to prove we can do it."
Rangers captain Lee McCulloch apologised to supporters after the disappointing performance, saying the players had no excuse for the struggles.
He said: "We owed a result to the fans, who turned up and made it another sell-out. We can only apologise to them.
"We've got a lot of new players, a lot of young players, and a couple of foreign players who don't speak English. But that's all excuses, isn't it?
"We really need to start picking up points now for the fans as well as ourselves.
"It's not acceptable so we are going to have to respond to it. We owe it to the fans, we owe it to ourselves, we owe it to the management and we owe it to everyone at the club.
"Drawing away from home at a club like Rangers isn't acceptable and, after getting beaten away from home, hopefully everyone knows now that it can't happen again."