Celtic conceded just 10 minutes after taking the lead
Brendan Rodgers accused his Celtic side of "lacking pride and desire" in their defending as their frailties were exposed again in a 1-1 draw in Suduva.
Rodgers said the Lithuanian champions' equaliser - a free header from a free-kick - was a cause for "real concern".
Similar errors proved costly for Celtic in their Champions League exit at the hands of AEK Athens.
"We seem to lack concentration, that is a problem, and our pride and aggression in terms of defending," Rodgers said.
"There has to be a greater desire not to concede from set-pieces."
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Rodgers' side have now won two of their past seven games - conceding in six of those - but will still be favourites to win next Thursday's second leg in Glasgow and reach the Europa League group stage.
The manager, though, was downbeat in his assessment of a performance that reinforced their need for defensive reinforcements, with continued uncertainty over Dedryck Boyata's future, and a new injury concern around Jozo Simunovic, who was forced off with an ankle knock.
"When you work with what you have, you have to try to improve it and make it better," Rodgers said.
"Games like that, especially away from home, you have to demonstrate that hunger to not concede, and it was too easy.
"It was a terrific ball into the box but we have to defend it better than that. It gave them a bit of oxygen in the game that our start should never have given them."
'I feel for the supporters'
Rodgers praised the contribution of 19-year-old winger Mikey Johnston, who created Olivier Ntcham's third-minute opener after a "great bit of skill" in his first European start.
But the Celtic manager felt his side "came off plan a bit in terms of running too much, blocking each other's space and we didn't really have the intensity and tempo we wanted".
He added: "I feel for the supporters. They have come all the way out here - about 200 of them - and we have to be much better than that.
"We are controlling a lot of the games, But against AEK we had four shots on target against us over two games where we were clearly a better team, but we conceded three goals. So it has to stop.
"Next week we want to finish off the job but we will need to play with a greater tempo than we did this evening."
Rodgers was unsure about the extent of an ankle injury sustained by Simunovic in the second half.
"He took a knock and landed awkwardly, so we will have to see how he is," he added.
'He's thrown in a grenade' - analysis
BBC Scotland's chief sportswriter Tom English on Sportsound
That is as down as I've heard Rodgers in a long time. It's interesting that he says he felt for the supporters - I can't remember him speaking like that before.
He's a very canny individual. He's got his message out there and it's a bit more pressure applied on the board. He's thrown in this grenade and this is a strategy to bend the club to his will again; as he has to do to protect himself. There is a game within the game going on at Celtic Park.
Former Scotland striker Steven Thompson on Sportsound
He's having a pop at his players and his board. It doesn't sound like a man who is particularly enjoying his work at the moment. Maybe the club didn't think they had to strengthen and Rangers caught them on the hop a wee bit. I think it has been complacency.
Source: bbc.com