Rangers edged the third-round replay when Jay Bothroyd climbed to meet Alejandro Faurlin's corner in the 76th minute and headed home.
Clarke knows that lapse in concentration proved costly for his side and feels his squad are feeling the effects of a busy few weeks, having won just two out of 11 games in all competitions.
"It is disappointing," he told the club's official website. "It's a competition we wanted to stay in as long as possible.
"I think on the night we had the better chances and Rob Green made a few decent saves.
"We went to sleep on a set-play and you get punished for that at this level.
"The squad has been stretched in recent weeks and the boys that have gone in have done their best. They've tried hard, they've worked.
"Maybe the little bit of luck we were carrying a few weeks ago has deserted us a little bit.
"But all we can do is knuckle down and get on with it."