Massimiliano Allegri's under-fire side headed to Glasgow on the back of a seven-game winless run, but cruised to a 3-0 victory in the crucial UEFA Champions League Group H encounter thanks to goals from Kaka, Cristian Zapata and Mario Balotelli.
The first two players benefitted as Celtic made a pitiful attempt to defend corners delivered from the right by Valter Birsa.
Neil Lennon's men also shipped a set-piece goal to Aberdeen’s Niall McGinn before securing a last-gasp 3-1 Scottish Premiership victory on Saturday, but Lustig insists such struggles are out of character.
"I don't think we have let one goal in from set pieces in during the whole season (before Aberdeen) and now we do it in the most important game of the season and it's not good enough," the Sweden international told Sky Sports.
The space afforded to Kaka and Zapata predictably led to fingers being pointed at Lennon's preferred zonal marking system, but Lustig once again referenced the defensive unit's previous resilience.
"I think we've conceded two or three goals in two years from set pieces and corners. I don't think the formation (zonal marking) is wrong.
"I don't know, the first goal is a free header from two or three yards so it’s not good enough."
Virgil van Dijk passed up a glorious opportunity at 1-0 when he smashed a close-range volley straight at Milan goalkeeper Christian Abbiati - and Lustig conceded such profligacy was an unfortunate feature of Celtic's campaign.
"Absolutely, it would’ve got the crowd cheering a lot - goals change games," he said when asked whether Van Dijk's miss marked a pivotal moment, as it came just two minutes before Zapata put the visitors 2-0 up.
"We've played five games in the group and we've just scored in one game so it's not good enough."
Ajax's surprise victory over Barcelona in Amsterdam means the consolation of a Europa League place is also out of Celtic's reach and Lustig's dejection was palpable.
He added: "We were hoping to get through to the last 16. If not that, we wanted to play in the Europa League but now it's over."
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