They gave themselves everything to do by going 2-0 adrift by the 12th minute.
Blues were much improved after the break but could have no real complaints as Wigan were worthy winners of the Fifth Round tie at the Lancashire FA ground.
The Latics now go on to face Manchester United away in the Quarter-Finals.
Joe Gelhardt, a first team squad regular who made his professional debut at Blues at the back end of last season, proved to be a big difference.
Blues went close through Adan George in the second-half and he also struck the crossbar, but they never really had the measure of their hosts.
From a fifth minute corner things went downhill as Kyle Joseph bundled the ball in from close range as Wigan packed bodies around goalkeeper Josh Bradley-Hurst in the six-yard box and dropped the ball right onto that area - a deliberate tactic they did all night.
Then in the 12th minute Gelhardt fired a penalty into the bottom right-hand corner after Nico Gordon took him out as he burst into the box on the left.
Blues were rocked by the double goal burst and struggled to contain Wigan, who were first to everything and out-hustled a strangely passive visitors.
Blues got their first shot in anger away in the 18th minute as Lucas Powell surged forward on the left and shifted the ball to George, whose low attempt from just outside the area was well gathered by Sam Tickle as it bounced just in front of him.
But Wigan kept coming at Blues and last ditch blocks by Powell and then Gordon stopped the home side scoring again as they broke through into the area to threaten.
Jensen Weir then curled a free-kick onto the face of the crossbar (29 minutes) before Bradley-Hurst produced a fine, flying stop to keep out a powerful header by Joseph.
Miller, who had earlier guided a left-footer straight at the 'keeper after gathering a clearance and running forward 15 yards trying to set himself ideally, had a glancing header from a corner cleared from the line in the 42nd minute.
But in the first minute of added-time Gelhardt struck, shifting the ball onto his left foot before launching an unstoppable 25-yarder that dipped into the top corner, giving Bradley-
Hurst no chance.
In the second-half Blues were a different proposition and their intent to shift the ball much quicker was evident early on.
They broke Wigan's press from the right-back position with Marcel Oakley via swift one-touch passing involving Miller and George that switched play to the left, but unfortunately Kyle Hurst couldn't get the ball out of his feet quickly enough to shoot as he was crowded out.
Then George went near, his shot taking a deflection that meant flashed wide of the post.
And when Oakley then drove forward there was another opening created, as George ran onto his pass down the inside right channel and prodded past the upright.
As Tate Campbell become more of a figure for Blues and Josh Andrews had more of an effect, with Hurst and George lively, they looked more like the team that had blown away Sunderland and caused problems for Barnsley in the previous rounds.
But in the 74th minute Wigan got their fourth, Gelhardt created a yard of space and cracked a shot that cannoned back off the crossbar; it came out to Sean McGurk who lashed the rebound in with real venom.
With 12 minutes left the luckless George knew it was not going to be his night when he angled a lovely curler from 20 yards only for it to clip the woodwork on the way over.
In the 82nd minute Luke Robinson did superbly to slide in and get his studs to the ball to stop George scoring from Powell's driven cross from wide.
Substitute Josh Williams also got in down the right of the area and fired just over on the run.
Blues had certainly fashioned more than their fair share of good opportunities in the second-half but just could not find that finish to go with their more vibrant display. It was the way they had been lacking to Wigan initially that ultimately paved their downfall and competition exit.
Blues: Bradley-Hurst, Oakley, Powell, Gordon, Browne, Walker (Dugmore 80), Campbell, Miller (Williams 70), Andrews (Zohore 76), George, Hurst. Subs not used: Rouse, Chang,