The Rapids hit the lead against Honduran outfit Real Espana when Jeff Larentowicz struck a brilliant first time shot outside the area against the run of play on the stroke of half-time.
It looked like Gary Smith's men would hold on for a snatch and grab victory but Espana's Julio Rodriguez volleyed in the equaliser in spectacular fashion with two minutes remaining to deny the visitors.
Despite squandering the lead so late in the match, Rapids defender Scott Palguta highlighted the fact that the club was sitting on top of Group B after two matches.
"I think when we all wake up tomorrow, we will realize we are still undefeated," Palguta told MLSsoccer.com. "But the consensus is that maybe we should have won the game."
Head coach Smith was proud of his players for showing plenty of spirit in a match played in extremely difficult conditions.
"It was a very different game than the one at the weekend," he said, referring to the 2-2 draw with Chivas USA on Saturday.
"We may be a bit disappointed about how the goal came about, but there were some tired legs out there and some terrific displays. The last 10 minutes was backs-to-the-wall stuff, but the lads showed determination and spirit in truckloads."