The injection of Australian midfielder Tom Rogic early in the second half was not enough to spark Celtic to a Europa League victory as they went down 3-1 to an in-form Milan side in Glasgow.
Bosnian midfielder Krunic headed the first and Brahim Diaz scored a neat second for the Rossoneri, before Jens Hauge added a late third, as they produced an efficient performance in Glasgow against the Scottish champions.
With Celtic reeling from a derby defeat to Rangers and weakened by a string of injuries, this match always looked unlikely to provide the succour for which they were hoping.
Milan was so in charge that Zlatan Ibrahimovic could effectively stroll through 65 minutes before being replaced, but they were hanging on after Mohamed Elyounoussi's header gave the hosts a surprise foothold until Hauge made sure.
Celtic wanted an early penalty when Albian Ajeti's shot hit Alessio Romagnoli, but it did not look to strike the Milan captain's hand, and Olivier Ntcham's follow-up strike was tame.
It was downhill from there for the hosts, with Milan snatching a 14th-minute lead when Samu Castillejo sent in a teasing cross from the right and former Empoli man Krunic headed beyond the dive of goalkeeper Vasilios Barkas, finding the left corner.
Jeremie Frimpong was at times lively for Celtic on the right, but Milan are eager to make their presence felt in this competition, despite having only edged into the group stage after beating Rio Ave 9-8 on penalties in their play-off.
Diaz got the second goal for Stefano Pioli's men in the 42nd minute, taking a pass from Theo Hernandez and showing nimble footwork before burying a low shot into the left corner.
Uruguayan winger Diego Laxalt sent a shot a yard over the Milan crossbar early in the second half as Celtic searched for a way back into the game.
Rogic was introduced into the action for Celtic after 64 minutes with Neil Lennon hoping the Australian's ability to break a game open could inspire the Scottish champions to a second-half fightback.
Ryan Christie's corner was nodded in by fellow substitute Elyounoussi in the 76th minute to give the hosts hope, but Milan were in no mood to be denied and Hauge finished well from Alexis Saelemaekers' pass in stoppage time.
What does it mean?
Pioli can reflect on a positive start and Milan are now unbeaten in 21 games in all competitions.
With Krunic and Hauge scoring their first goals for the club, there was much to enjoy, even if they will feel they should not have allowed Celtic a sniff over those closing 15 minutes.
Diaz decisive, Castillejo class
Diaz has played for Manchester City, Real Madrid and now Milan by the age of 21, and his finish was one of an accomplished player. However, Castillejo was the Milan attacker who most caught the eye, his cross for the opener being perfect for Krunic. Castillejo barely wasted a pass and was always looking for a killer ball, playing four crosses, three of which were rated as good deliveries by Opta.
Will Zlat do?
Ibrahimovic could not make his presence felt - or perhaps he was simply not in the mood. The Swede might have revelled in the atmosphere provided by a full Parkhead, where European nights can be seriously special - as Milan found out when they lost to the Scots in the Champions League 13 years ago.
But behind closed doors in Scotland, his influence was negligible; he played one key pass, found his target with just 75 per cent of all passes, did not take a single shot and won only 33 per cent of his duels.
Celtic travel to Aberdeen in the SPL on Sunday, before heading to Lille in the Europa League next week. Milan have back-to-back home games, against Roma in Serie A next Monday and three days later against Sparta Prague in this competition.