Neil Lennon said Celtic's defeat by Legia Warsaw "might have been on the cards" because of the lack of investment in the side and his successor Ronny Deila's lack of time in the job.
The Parkhead outfit were torn apart as their Polish hosts triumphed 4-1 on a night that could have turned out even worse for Deila's men.
Legia failed to convert two second-half penalties after Efe Ambrose had been red-carded two minutes before the interval, as Celtic "lost their heads", according to their manager, who also questioned his players' commitment.
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It was a sobering night for Celtic, who now need a remarkable turnaround in the second leg at Murrayfield in Edinburgh on Wednesday.
For Lennon, though, who stepped down earlier this summer after four years as manager at Parkhead amidst suggestions he was concerned by cuts to his budget, the result did not come as a surprise.
The Northern Irishman failed to get past the third qualifying round of the Champions League in his first season in charge, losing 3-0 away to Portuguese outfit Braga in his first competitive match after being handed the job permanently in the summer of 2010, before progressing to the group stages in his next two attempts.
He said: "I wouldn't say it was inevitable, but I think it might have been on the cards.
"There's been no investment at the minute in the team and Ronny really hasn't had much time to bed himself in with [assistant manager] John Collins and to get to know the players.
"Those qualifiers are always really tricky. They're not out of it yet, but they're going to have to play supremely well to go through now."
Celtic will drop into the play-off round of the Europa League unless they can pull off an incredible comeback at the home of Scottish rugby next week.
However, despite the club's strong balance sheet mitigating the financial requirement of qualification for the Champions League, Lennon believes progress is "imperative" due to the make-up of this season's Premiership, which will be without Rangers, Hearts and Hibernian.
He explained: "[A Champions League run] is always important, it gives the fans and the players something to look forward to, and, of course, there's the money side of it as well. The club is financially healthy, so I think they can maybe take a hit on not making the Champions League this year; I don't think it will be disastrous for them in the long-run.
"But, certainly, from the football angle, it's imperative that they stay in there and qualify. It's incredible, you've probably got three of the biggest teams in Scotland playing outside the top division. It's probably unprecedented in the history of Scottish football."
While Lennon refused to blame Deila for the outcome of the match, Jakub Kosecki, the Legia substitute who scored twice in the closing stages, believes the Norwegian and his players were architects of their own dramatic downfall in the Pepsi Arena. The Poles and their manager, Henning Berg, had been subjected to heavy criticism after they required a late equaliser in their previous home match in the competition, against Irish side St Patrick's Athletic.
By the final whistle, though, it was the small band of Celtic supporters who had made the trip to Poland that were asking serious questions of their players and management team.
Kosecki said: "I knew it was going to be an easy game for us if Celtic took us lightly, and I think they did. I knew it because I know my team very well and we are a good team."
"Not everyone appreciates us, but I'm confident, although it's only half way for us with Celtic. We have a good lead, but we can't take them lightly in the second leg. We must play as well as in Warsaw, maybe even better, to get through."
Meanwhile, Kosecki's team-mate Ivica Vrdoljak - who missed the two penalties that would have put the tie beyond Celtic's reach - said he wouldn't beat himself up over his profligacy.
However, he echoed his colleague's sentiment that there is still a lot of work to be done before they can progress to the next round.
The Croat said: "Ivan Rakitic once missed four penalties in a row, but still got a move to Barcelona. Listen, in life there are far worse things that can happen than missing a penalty.
"We have achieved a great result, but we must remember we are only at half time. We have to be smart in Scotland for 90 minutes."