And the fall did not stop there. They were in League One before finally hitting rock bottom, although after a couple of failed promotion attempts it appears the West Yorkshire outfit are on the rise again under impressive young manager Simon Grayson.
There is certainly enough optimism around Leeds just now to ensure a scramble for all 9,000 tickets they have been given for Sunday's eagerly-awaited FA Cup tie at Old Trafford.
And, although he knows the reception he faces will be decidedly frosty at one end of the ground, Carrick is eager to get out in the middle.
"Experiencing those types of feisty atmospheres are why you play football," he said.
"Rivalries like that add extra spice. It is great for the fans and good for the players.
"No matter where you play, or whether the atmosphere is for or against you, it is a great feeling to play.
"Besiktas were very hostile when we went there earlier this season but it was still terrific to play in.
"Leeds are bringing a lot of fans and we are looking forward to it. It should be a cracking game."
Although history dictates any match between the biggest two teams who represent the red and white roses will have an extra edge, the reality of the situation suggests a comfortable home win.
As Leeds were unable to break their Old Trafford hoodoo when they were competing on level terms, their current status in the third tier of the English game hardly suggests a first win at the home of their bitter rivals since 1981.
It means United should take a small step forward in another competition, having already secured a Champions League knock-out meeting with AC Milan, a Carling Cup semi-final with Manchester City and second spot in the Premier League, two points adrift of current pace-setters Chelsea following last night's five-goal hammering of Wigan.
By general agreement, their latest success represented United's best performance of a campaign blighted by injury, in addition to the major adjustment required following the departure of Cristiano Ronaldo.
But now they have set a suitable standard from which to push for honours, Carrick is expecting far more convincing displays during the second half of the season.
"We have not hit top form all season, especially at home," said Carrick.
"We have just been doing enough to get through. We know we are better than that and now is the time to do it.
"It is a busy time until the end of the season. We need to get a run going and start playing some good football.
"We are in a good position in the league, we have the FA Cup coming up, we are through to the Champions League last 16 and reached the Carling Cup semi-finals.
"We have done as much as we can so far. Now is the time to really drive on and achieve things again. That is why we are here."