Northern Ireland started brightly after the break, helped by half-time substitutes Corey Evans, Warren Feeney and Grant McCann.
Steve Jones then hit the post for the home side with Bournemouth's Warren Feeney scoring the decisive and winning penalty.
Healy replaced Warren Feeney and the substitute made an immediate impact with a low shot which had Mikkelsen at full-stretch.
Jonny Evans and Warren Feeney joined Northern Ireland's long absentee list on Tuesday before news of McCartney's international retirement came through.
Midfielder Sammy Clingan had a dead leg, defender George McCartney was suffering from blisters and forward Warren Feeney reported a slight virus.
The hosts went close on 51 minutes when Petr Cech kept out Warren Feeney's shot and Chris Brunt fired the rebound over.
Warren Feeney finished from close range after 10 minutes but Poland levelled when Maik Taylor failed to keep out Ireneusz Jelen's shot.
He cited ex-Bluebirds Roger Johnson and Warren Feeney as players to have suffered the sort of hip problem Ledley, 22, has complained of.
Bournemouth's Warren Feeney was then left to score the winning penalty.
However, two second half goals in four minutes put United in control as Lee Wilkie and Warren Feeney headed home expert crosses from Paul Dixon.
Worthington made two half-time changes with Crewe's Michael O'Connor coming on for his debut in place of Damien Johnson and Lafferty making way for Warren Feeney.
Jones will have his fingers crossed that his striking options are not limited any further, as Warren Feeney is cup-tied and Robbie Fowler remains on the long-term injury list.
George McCartney will be available to play in defence after missing training on Monday because of blisters while Warren Feeney is also expected to be available despite a minor virus.
Northern Ireland boss Nigel Worthington made two changes from Saturday's 1-0 defeat in Latvia with Brunt replacing Stuart Elliott in left midfield and striker Warren Feeney coming in for Kyle Lafferty.
Hearts were missing as an attacking force, but they comfortably survived during a scrappy ending to the half, which saw Warren Feeney booked by referee Eddie Smith for a late challenge on Balogh.
Roy O'Donovan was thrust straight into the United line-up following his loan move from Sunderland and his excellent headed flick narrowly evaded the sliding Warren Feeney right in front of the Accies' goal.
Ryan made up for his earlier mistake in the 57th minute by clearing a shot from Warren Feeney off the line before Doncaster sent on Robert Gill as a substitute on the hour.
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