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Doncaster, who play two tiers higher than Kidderminster in England’s football pyramid, fell at the first hurdle in the famous competition, losing 3-0.
The defeat came just seven days after Rovers were beaten 6-1 away to MK Dons in League One – their fourth league loss in five matches.
McCann, who finished his playing career at Linfield, the club he supported as a child, has been in his position as Doncaster boss since 2023 and guided them to the 2024/25 League Two title.
The 46-year-old has won 87 and drawn 38 of his 193 matches in charge across a second spell as Rovers manager.
With Doncaster currently sitting just one point above the relegation zone, pressure appears to be mounting on McCann, who opened up on the struggles of management during tough times.
"The supporters pay their hard earned money to follow us, there’s almost 700 of them there coming three hours down the road,” said McCann on BBC Radio Sheffield. “It hurts, it really hurts, when they’re telling me I’m being sacked in the morning, telling the players they’re not fit to wear the shirt.
"I brought every single one of those players to the club so that’s another indictment on me.
"The boys are really stinging in there, massively hurting, and what I do know in football is you’ve got two choices: you throw it all up in the air and don’t carry on, or you stick together and get through the dark times.
"It’s a tough period for us, we’re not performing well enough, not doing the basics of football well enough.
"We’ve been pretty successful since we’ve been here in the four years and one thing about football is people want to hit you and knock you when you’re down...it’s a lonely place when you lose games because nobody wants to text or ring you.
"When you win, your phone is off the hook...I try not to act like that, I try to act as calm and positive as possible, I don’t get too high or low with defeats, but I understand today is a really disappointing day for the football club, for us, for the fans.”
Doncaster will be back in action on Saturday when they host Leyton Orient and Belfast-born McCann, who earned 39 caps for Northern Ireland, is determined to battle on.
"Hurt, really, really hurt (is what you feel when hearing those chants),” added McCann. “What’s gone is gone at this football club, but what I will say is you can only affect what’s in front of you.
"The way of the world, particularly with social media, people want to knock you all the time whether you win, lose or draw.
"The fans are entitled to their opinions, all we can do is make sure we’re united as a group, there’s a real siege mentality and we stick together like we always do.
"Do you back off into a dark corridor and try to block it off, or do you stand up and fight? I have always been the latter and been one to face the consequences.”