He was named on the bench but pulled out on the morning of the game.
McGeechan explained his withdrawal, saying: "Danny is just sore. It's a three-day recovery and it was just too quick, which is why we decided not to have him on the bench today.
"He has played his first game for months and, in the end, it was too quick to have him back.
"There is no problem - he's fit. It was just the timescale was too quick. There is certainly no problem."
Defeat does not help Wasps' chances of qualifying through their pool but McGeechan was happy with the performances of his young players, particularly full-back Lachlan Mitchell.
He added: "We played well to get the (losing) bonus point here and the forwards were outstanding today. There were a lot of players there playing in a competition like this for the first time and I thought they did well, particularly up front."
Gloucester head coach Dean Ryan, meanwhile, was satisfied with his side's victory which puts them in prime position in Pool A of the competition.
They face Welsh region Newport Gwent Dragons later this month at home where a win will probably be enough to get them through to the knock-out stages.
First, though, the Cherry and Whites enter the Heineken Cup next Saturday with an opening home tie against Biarritz.
Ryan said: "I am happy with that win. We lost in the last minute last year and it was almost set up for a repeat.
"When you play Wasps, you want the result. Performances are there week in and week out but if you have a ding-dong against Wasps, you are happy to come out on top.
"This gives us a chance to push some resources at this competition in the later games.
"We will look at this and think we let them back into the match but I'm pleased with the win."