Goals within three minutes of each other from Hulk and Sergei Semak as the match in a sub-zero Petrovsky Stadium entered the final quarter put a significant dent in the Reds' ambitions.
Carragher, a veteran of 149 European outings, felt the side showed a lack of experience - despite him, Steven Gerrard, Lucas Leiva, Martin Skrtel and Jose Reina having made 435 combined appearances in continental competition.
"It was frustrating because up until they scored it had probably been a perfect European night in the way we dealt with the onslaught in the first half and creating a few chances," he said.
"Second half we looked in control but that's European football, we had a few experienced lads and some young lads and you have to learn but you have to learn quickly - especially at this level.
"That is a typical European night because you think you are in control and - bang - you are 2-0 down with a mountain to climb.
"But it is a mountain the club have climbed in the past and we have to look to do again in a week's time.
"It was a disappointing night but we have a week to dust ourselves down and try to come back and if we could do it it would be a great European night."
Top scorer Luis Suarez missed a number of chances, with manager Brendan Rodgers admitting he could have had a hat-trick in the first half, but Carragher said the Uruguay international should not be held responsible for the result.
"Everyone creates chances - we never put them in - but you can't be conceding goals like that, especially at that time of the game in the 70th minute when you have everything under control," added the centre-back, who will retire at the end of this season.
"There is no point in looking at the strikers, we have to look at ourselves as a team defensively in that situation.
"The first one is a great goal to be fair but you can always defend things better but the second one is a poor goal all round for us.
"They are big favourites now, of course they are, but it will make for a good atmosphere at Anfield next week and if we can get that first goal the place will be bouncing."
Rodgers had built up the week, which began with defeat at home to West Brom and ends on Sunday with the visit of his former club Swansea, as a significant one.
But Carragher said they could not afford to focus on isolated sections of the season.
"It is massively important we get something from Sunday's game but it doesn't matter if it's this week, last week - every week is a massive week for Liverpool," said the 35-year-old as the Reds head into the weekend looking to end a run of five matches without a win.
"It could have been a great week with results at City and Arsenal (both 2-2 draws which probably deserved better in the preceding week) but this is the flip side of it.
"We have to get out of this little mini-slump we are in very quickly.
"Inconsistency has been a problem for us not just this season - it's not Liverpool's problem this season or Brendan Rodgers' problem - it's been a problem for three or four years.
"That is down to ourselves, the manager and coaching staff to get ourselves out of it because it's been going on a while now."
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