Ibrox defender Lorenzo Amoruso claimed he was fouled by Dirk Lehmann just seconds before the German supplied the header for James McFadden to prod over the line.
That proved to be the only goal of the game in an eventful 90 minutes during which time both sides squandered chances in front of goal.
But the Rangers boss insists Motherwell deserved the three points for being the better side whether Amoruso was fouled or not.
He said: "It was difficult to say. Lorenzo said that he had been fouled and Craig Moore backed that up. The referee said that the striker was on the wrong side of Lorenzo and was only looking for a way out. The defenders certainly feel that it was a free-kick but we are not using that as an excuse because of the way that we played."
McLeish added: "I thought the home side deserved to win we started okay, but then Motherwell carved out the better chances in the first half. They won the individual battles and this was a game that we have to look back on and say 'have we learned from it?' We have been on a phenomenal unbeaten run for a long time and now we have to start all over again, but I'm sure that we have the character to do that."
Amoruso showed his commitment to the team in his own way by refusing to be substituted after picking up an injury in the last 10 minutes of the game. Despite limping heavily, the Italian snubbed McLeish's offers to be replaced and opted to move up front instead in search of the equalising goal but McLeish admits he was lucky he didn't cost Rangers a second goal.
He said: "He was limping heavily and we nearly got caught out for the second goal and I was planning to put another player up front anyway because we had to gamble. But he moved up front and waved to us to say that he was okay."
Motherwell boss Terry Butcher revealed that his own players admitted their winning goal could easily have been given as a free kick for the opposition instead.
But the three points earned against the league-leaders eventually allowed the Fir Park side to haul themselves off the bottom of the table and Butcher insists he is more than willing to take advantage of the luck which is now coming Motherwell's way.
He said: "Dirk (Lehmann) said that it was a possible foul and, if it the same incident had come when we were on our bad run, it would probably have been given as a free-kick. But Lady Luck was with us this time it wasn't a pretty goal but I'd take anything as long as it goes in the back of the net.
"I said to the players that it doesn't matter if it's the scruffiest, messiest goal because it could turn out to be the best goal of the season.
"Our game plan was to not allow them to settle and it isn't rocket science. If you allow teams like Rangers and Celtic to string together passes and become comfortable on the ball, then you're in for a doing. We set our stall out to frustrate them and I knew that it could end up one on one so I told the players, if that happens, stand up and be counted."
MOTHERWELL: Dubourdeau, Kinniburgh, Corrigan, Partridge, Hammell, Adams, Cowan, Leitch, Pearson, McFadden, Lehmann.
RANGERS: Klos, Malcolm, Moore, Amoruso, Muscat, Ricksen, Ferguson, Lovenkrands, de Boer, Mols, Caniggia (Dodds 72).
Referee: W Young (Scotland).