However, Dungannon striker Morgan said Glentoran's Sean Ward had handled the ball just before he did.
Edu had earlier had a goal disallowed after his team-mate Kenny Miller had handled the ball.
Soresenen completely mis-handled the ball into the net, leaving the Danish keeper head-in-hands with embarrassment.
BBC: SPORT | Football | Premiership | Middlesbrough 1-3 Aston Villa
The Republic lost on aggregate to an extra-time goal when France's Thierry Henry handled the ball in the build-up.
"Everybody thought Chris Morgan had handled the ball and that the referee had awarded a free-kick to us, " said Gillespie.
The goal came just after Tapuwa Kapini had saved a penalty from Lwazi Masiya after Dumisani Mpofu had handled the ball inside the box.
West Ham's defence has been impressive this season and even when it looked as though Ferdinand had handled the ball, Fulham's penalty appeals were waved away.
Midway through the second half Sevilla claimed their own penalty, arguing Senderous handled the ball in the area, but that call also went unheeded by referee Eric Braamhaar.
Henry twice handled the ball before crossing to William Gallas, who scored the equaliser against the Republic in the play-off in November to put France into next year's finals.
Ipswich's keeper handled the ball outside his penalty area following a hopeful punt forward and three minutes later replacement keeper Arran Lee-Barrett was picking the ball out of his net.
Fittingly given his impressive start it was McIndoe who gave Doncaster the lead after Ridgewell was adjudged to have handled the ball in the area following a James Coppinger's cross.
BBC: SPORT | Football | League Cup | Doncaster 3-0 Aston Villa
Goodwin had a powerful shot blocked and deflected out for a corner, then Duberry handled the ball inside the Saints box from the resulting set-piece to hand Accies a lifeline.
Bamba capped a dismal night for his side when he handled the ball in the box, Craig's penalty deflecting off the unlucky Smith and into the back of the net.
Motherwell spurned a fabulous late chance to draw level on the night at Fir Park, watched by a crowd of 9, 105, when Anders Moller Christensen handled the ball in the box and was sent off, joining Espen Ruud who had been red carded 10 minutes earlier.
Trapattoni's side lost the first leg in Dublin 1-0 but were leading 1-0 in Paris before Henry handled the ball and squared for Gallas to nod in a goal that sent France to the 2010 World Cup finals in South Africa and left the Republic heartbroken.
The Republic of Ireland lost out on a place in South Africa when former Arsenal striker Henry handled the ball in the build-up to the decisive extra-time goal which earned France a 1-1 draw on the night and an aggregate 2-1 win in last year's play-offs.
However, the ball was handled in a goalmouth scramble and the opportunity was lost.
It was a bizarre goal and a bit fortunate, but we thought Mido's shot might have been handled by a defender before the ball ended in the net.
The ball was handled by spectators, which should have denied Wales the right to take a quick throw-in, but Wales captain Matthew Rees was handed a different ball by a ball-boy and passed in to Mike Phillips peeling round the blind side.
As could Zdenek Zlamal when Lita stepped up to take England's penalty after Hubnik handled as Nugent looked to lift the ball over the otherwise outstanding Czech skipper.
BBC: SPORT | Football | Internationals | Czech Rep U21 0-0 England U21
Fraser was next to fluff a penalty attempt, slipping as he struck the ball after Scott Morgan handled at a ruck, but the visiting fly-half made amends in the 20th minute as the Blues were punished for another breakdown offence.
The alarms rang in the 18th minute when both Jose Enrique and Coloccini failed to clear under pressure from Lee in the left-corner before the ball fell to Bolton old-boy Nolan who handled in his attempt to ease the pressure.
Higdon had the ball in the net later but was adjudged to have handled.
Molloy scored a penalty on seven minutes after a Stuart King's free-kick had been handled and he fired home his second after a loose ball fell to him in the box.
Referee Adrian McCourt adjudged that Mark Gracey had handled inside the area but Neill's spot-kick was blocked by Plummer, and the ball was then stabbed against the post and eventually cleared.
Brazil defender Juan was one of five other players booked but it could have been worse when he handled 40 yards from goal from a long ball seeking to release Real Madrid's Cristiano Ronaldo clear down the right.
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