Having dropped out of the Champions League at the hands of AEK Athens, Celtic have a chance to keep their European campaign alive in the Europa League but Rodgers was not happy with their display in Lithuania.
An early goal from Olivier Ntcham should have put Celtic in control but the Scottish Premiership champions switched off to allow Ovidijus Verbickas to restore parity.
Finding another way through proved impossible for Rodgers' men and although they have a vital away goal, Rodgers knows there needs to be drastic improvements if they are to go far in the competition.
"We have to be much better than that," said the Hoops boss.
"I thought we made real hard work of it. It was a really good start to the game.
"That gave us the perfect start and then after that we came off plan a wee bit in terms of running too much and blocking each other's spaces.
"We didn't really play with the tempo and intensity that we wanted. We gave away a soft goal which is a real concern. We weren't giving away many chances but we didn't defend the set-piece well enough.
"It's a European goal away. We go back next week to finish the job. I always look at the performance level and it wouldn't have been quite how we would have wanted."
Rodgers added: "We seemed to lack concentration, which was a problem for us, and we lacked pride in terms of defending – I think that’s pretty clear.
"Games like that, especially away from home, you need to demonstrate that hunger not to concede. It was too easy.
"We need to go away and work even harder on it. The players and coaches will take all the responsibility and we have to improve that side of it."