McCall's men were knocked out of the competition thanks a 2-1 loss at the hands of the Sky Bet League Two side at the Northern Commercials Stadium.
James Hanson and Haris Vuckic had promising scoring chances for City in the first period but Accrington attacker Romauld Boco, who earlier had hit the bar, netted on the half hour mark to give the visitors the half time lead.
Matthew Kilgallon levelled for City midway through the second period with his first goal for the club but Jordan Clark responded for Stanley ten minutes from the end with a well-taken winner.
McCall said: "It was hugely disappointing for us today (Saturday) - both in terms of the result and the performance.
"We didn't play with enough energy or tempo. Credit to Accrington, I thought they fully deserved their victory.
"Even when we get it back to 1-1, we don't do enough to go on and get that winner ourselves.
"We didn't take charge of the game - we seemed happy to let it flow along.
"This is probably the first time this season that I've been unhappy with our result and performance from a single match.
"We knew Accrington would raise their game - some of their best performances this season have come in the cups - and is frustrating that we've not shown the right attitude and endeavour.
"They have won too many of the key battles.
"We can't get back into the cup now - we're out and we're hugely disappointed with that - but we must lick our wounds and move on.
"It is how we react now on Wednesday (Morecambe, Checkatrade Trophy) and on Saturday (Rochdale in the league).
"We need to response in the right way after this disappointment."
McCall made six changes in total for the visit of Accrington, with Vuckic, Nathan Clarke, Rory McArdle, Daniel Devine, Filipe Morais and Mark Marshall all coming back into the side.
The City chief added: "I think some of the players out there looked a bit rusty, that is perhaps understandable as you need games to get back into the flow.
"I thought every player named in the side would be good enough to help us get through. We weren't (good enough) because there were too many disappointing individual performances.
"That goes not just for the lads coming into the side though, I think I'd be struggling to name a player who played to their potential this afternoon.
"Realistically, if you want to be successful, you have these sort of afternoons maybe three or four times a season maximum. This is our first one we can really say we've had so far this campaign - we don't want many more.
"It is a fact of life, you can't win all the time and you can't play brilliantly all the time. When you do have occasions like this, however, it is important how you bounce back.
"Just because we've lost today, it doesn't mean we have a bad squad or a bad dressing room. It means we've had a bad afternoon.
"We can't dwell on this. We have to come in on Monday and be bright and ready to respond properly at Morecambe on Wednesday and then against Rochdale on Saturday."