Following an action-packed encounter at Accrington's Wham Stadium, City's League Two hosts eventually booked their place in round two thanks to a marathon 11-10 shoot-out victory.
Ahead of penalties, McCall's men had dominated the tie for large periods, creating a whole host of scoring chances, although they were grateful for a penalty save at the start of extra time from 'keeper Colin Doyle.
On his first competitive start in City colours, Jordy Hiwula went close to netting on more than one occasion, while Nathaniel Knight-Percival and Nicky Law fired over from great positions at different points in the game.
Ahead of his sending off in the latter stages of the second period, Accrington 'keeper Elliot Parish impressively repelled efforts from Hiwula and City substitutes Mark Marshall and Filipe Morais during the tie.
With substitute goalkeeper Aaron Chapman on for Accrington as Parish's replacement for extra time and final stages of the second half, City struck the post twice through Marshall and Romain Vincelot.
A clearly disappointed McCall was able to take some positive from the way City had controlled the contest for the most part but he was still fully aware of his side's need to be more clinical in front of goal.
McCall said: "It should never have gone to penalty kicks really.
"We've dominated for large parts of the game and created a bucket load of chances. We just couldn't do the most important thing in football though, and that's put the ball in the back of the net.
"Both of their goalkeepers have made some terrific saves, we've hit the woodwork twice, but we've also squandered some really good chances ourselves.
"I'd say 90% of our performance was really good - I'd be more concerned if we weren't creating these chances - but we have to start taking them.
"We know that though, and we can't let tonight's (Tuesday) result affect what we are striving to do.
"In lots of ways, the last two performances we've had have been really good.
"Fair play to Accrington, they have stuck in and defended bravely but on another day we should have had four or five goals.
"We have to dust ourselves down now and prepare for two important away games in the league (Peterborough United and Milton Keynes Dons) that are coming up."