Paul Hartley, Jan Vennegoor of Hesselink and Shunsuke Nakamura all left the club in the summer.
Meanwhile, Jan Vennegoor of Hesselink has been an able replacement for John Hartson.
BBC: SPORT | Football | My Club | Celtic | Celtic's title relief
Jan Vennegoor of Hesselink fired Celtic into a first-minute lead with a shot from the edge of the box.
Hull's equaliser came from the penalty spot after Sol Campbell was adjudged to have brought down a seemingly offside Jan Vennegoor of Hesselink.
The home side had a deflected Tom Cairney shot and a header wide by Jan Vennegoor of Hesselink to show for their efforts.
Jan Vennegoor of Hesselink bundled in the second goal, Aiden McGeady powered home the third from 25 yards and the fourth was volleyed in by Darren O'Dea.
Jan Vennegoor of Hesselink struck the winner in the dying minutes against 10-man Stoke at the weekend to haul themselves out of the Barclays Premier League relegation zone.
The Gunners took the lead through Andrey Arshavin after 14 minutes but Jimmy Bullard leveled with a penalty after 28 minutes when Sol Campbell fouled Jan Vennegoor of Hesselink.
The Potters would have moved up to seventh in the Premier League with victory at the KC Stadium, but were denied a point by a late strike from Jan Vennegoor of Hesselink.
Chelsea pair Arjen Robben and Khalid Boulahrouz, Celtic duo Evander Sno and Jan Vennegoor of Hesselink, Wigan's Danny Landzaat, Robin van Persie of Arsenal, Liverpool striker Dirk Kuyt and Blackburn defender Andre Ooijer have all received call-ups.
BBC: SPORT | Football | Internationals | Van Persie out of Holland squad
Jan Vennegoor of Hesselink battled with a posse of Killie defenders at the edge of the penalty box and when the ball broke to Maloney, he curled it first time into the top corner of the net.
And, although the early goal visibly rocked Celtic's confidence, the home side began to take control of midfield and Scott McDonald fired just over from 20 yards, while a head flick from Jan Vennegoor of Hesselink drifted just wide.
Aquilani placed a shot just wide after an overhead ball from Ryan Babel was only half-cleared but Hull did create a chance of their own when Jan Vennegoor of Hesselink bulldozed through the Liverpool defence before heading straight at Pepe Reina.
In bright sunshine, the present side, managed by Neil Lennon, ran out easy winners with a Lee Naylor hat-trick, doubles from Gary Caldwell and Scott McDonald, and with Jan Vennegoor of Hesselink, Aiden McGeady, Massimo Donati and Simon Ferry also on the scoresheet.
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