Accies had failed in a bid to sign Iriekpen in January after he left Scunthorpe United.
Unsurprisingly, Celtic were unchanged from the side that thumped Hamilton Accies 4-0 at the weekend.
As the impressive Accies tired, Tomas Cerny made excellent stops from Steven Davis and Nacho Novo.
"We made a few changes today because we've been conceding horrendous goals, " said the Accies boss.
Accies goalkeeper Tomas Cerny launched forward a free-kick from just outside his own area.
Accies made four changes with Canning, Buchanan, Nigel Hasselbaink and Tom Elliot earning starts.
But the visitors' defence was resolute and Accies held out for a much-needed three points.
Accies took the lead through Simon Mensing with Martin Canning seemingly in an offside position.
The fines stem from clashes after Accies' 2-1 Scottish Premier League victory on 6 December.
Accies enjoyed a brief flurry but they still struggled to create any decent chances.
Accies broke the deadlock when Brian Easton headed home from an Alex Neil free-kick after 25 minutes.
Dougie Imrie forced a fine save from Accies' Tomas Cerny and Offiong missed another chance before scoring.
Accies rarely threatened, although Jim McAlister and Jonathon Routledge both had efforts denied in the second half.
He was a target for Hamilton Accies and Hibernian last summer, but Falkirk rejected bids from both clubs.
Before Accies started pre-season training on Monday, they also had added three signings primarily for their under-19 squad.
David Graham scored a spectacular volley against the run of play to draw Accies level after 34 minutes.
David Elebert could have claimed the points for Accies in the dying minutes, but his header inched wide.
BBC: Hamilton's David Elebert (left) tussles with Sone Aluko
Rudi Skacel gave Hearts a 32nd-minute lead, dipping a volley towards the Accies goal from 18 yards out.
Aberdeen pressed hard for an equaliser and Mark Kerr and Mulgrew were frustrated by last-ditch defending by Accies.
Goalkeeper Scott Flinders touched Akins' shot onto the post before the striker missed an excellent chance to give Accies the lead.
Danny Grainger's late goal gave St Johnstone a 2-1 victory, leaving Accies seeking their first win since August.
The Accies forward dispossessed Lee Cox, dribbled round a few players and cracked a left-foot shot into the net.
Simply, Inverness had not troubled Tomas Cerny sufficiently in the 90 minutes and Accies' season is off and running.
Accies' Flavio Paixao twice went close, hitting the side netting before seeing a curler saved well by Allan McGregor.
There was nothing suspect about Accies' third goal, with David Graham drilling in a fine shot from 15 yards.
Maros Klimpl and Sheridan both tried their luck with long-range drives, but failed to bother Accies keeper Tomas Cerny.
Twelve football matches were postponed in Scotland last weekend, including the SPL meeting between Hamilton Accies and Dundee United.
With 17 minutes remaining, Graham crossed for McArthur to head over as Accies searched in vain for a leveller.
"He hasn't told me that he has had enough, " said assistant boss Mjallby after the 2-0 win over Hamilton Accies.
Scotland Under-19 goalkeeper Andy Kennedy, 18, returned to New Douglas Park three years after being sold by Accies to Celtic.
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