Gareth McAuley is likely to be drafted into the defence with Jonny Evans switching to left-back.
Jonny Evans' absence opens the door to Manchester City's McGivern - currently on loan at Leicester City.
He is battling a calf strain with his replacement against City, Jonny Evans, also carrying a hamstring problem.
Bjornsson was booked for a late challenge on Jonny Evans on 19 minutes.
It follows the news that defenders John O'Shea and Jonny Evans have been ruled out of action until January.
Home defender Jonny Evans was shown a straight red card in the second half for a lunge on Stuart Holden.
Manchester United defender Jonny Evans will sit out Wednesday's game against San Marino, after picking up his second yellow card of the campaign.
Jonny Evans squandered another good chance as NI pressed before Slovenia went ahead through Milivoje Novakovic's close-range finish on 84 minutes.
Berbatov's winner came after United defender Jonny Evans was shown a straight red card for a tackle on Bolton's Stuart Holden.
Pompey did manage to carve out one chance and it took an alert Jonny Evans to clear Jamie O'Hara's goal-bound effort.
Jonny Evans headed straight at Bozovic from a corner before Manchester United team-mate Oliver Norwood came on for his senior debut.
Jonny Evans and Warren Feeney joined Northern Ireland's long absentee list on Tuesday before news of McCartney's international retirement came through.
Jonny Evans slid in to restore the lead and Northern Ireland went further ahead when Michal Zewlakow's backpass bobbled past keeper Artur Boruc.
The 20-year-old Manchester United player, currently on loan at Plymouth Argyle, came in following the withdrawal of injured pair Jonny Evans and Chris Baird.
Cristiano Ronaldo made his comeback after ankle surgery and almost set up Jonny Evans for a late winner, only for the youngster to head against the post.
Kyle Lafferty and Jonny Evans went close for the visitors in the first half while Niall McGinn missed an open goal just after the break.
Jonny Evans was also forced to come off before the end of the victories over Birmingham and Wigan as he continues to feel the effects of a long-standing ankle problem.
Manchester City teenager Weiss was the architect of Slovakia's goal, dribbling past Jonny Evans and his cross gave the unmarked Sestak the simple task of slotting in from two yards.
His list of injured defenders includes England internationals Gary Neville and Wes Brown, who both limped out of Saturday's game, plus longer-term defensive casualties Rio Ferdinand, John O'Shea and Jonny Evans.
Fit-again centre-half Rio Ferdinand may replace Jonny Evans to make his first Premier League start of the season, while keeper Edwin van der Sar and striker Dimitar Berbatov are almost certain starters.
BBC: Sir Alex Ferguson warns Man Utd ahead of Liverpool game
Things got even more interesting when defender Jonny Evans picked up an injury with 15 minutes left but was forced to play on as United had used up all three of their substitutes.
Rio Ferdinand and Jonny Evans are ruled out, but Ferguson hopes Serbian center-back Nemanja Vidic will recover from illness for Wednesday's Champions League trip to Wolfsburg, with United needing a point to finish top of Group B.
United had chances to increase their advantage with both Rooney and Nani close to adding a fouth, but it was Arsenal who claimed a late consolation when Thomas Vermaelen's shot found the net after taking a deflection off Jonny Evans.
United - with only one clean sheet to their name this season - fielded centre-halves Wes Brown and Jonny Evans - in for the injured Nemanja Vidic and Rio Ferdinand - but it was their front men who were the busier pairing.
Fernando Torres had a chance to wrap the game up before Mata cut inside Jonny Evans and struck on goal from six yards out but De Gea stuck out a leg to get a vital touch and divert the ball round the post.
Worthington brought Manchester United teenager Oliver Norwood on for his senior debut in the second half while his Old Trafford team-mate Corey Evans and Jonny Gorman were also introduced after the break.
Gloucester made a real mess of the re-start and Gavin Henson - who did his chances of a Wales recall no harm - and Ian Evans gave Jonny Vaughton a run at the corner.
They also signed another United this week, Northern Ireland midfielder Corry Evans, younger brother of Jonny, on an initial six-month loan deal.
Corry Evans joins his brother and club-mate Jonny in the squad.
BBC: Craig Cathcart in NI squad but no place for Pat McCourt
Casement is currently without a club after being released recently by new Ipswich Town boss Roy Keane while Evans is at Manchester United along with his older brother Jonny.
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