Arsene Wenger's men played a full part in an absorbing Emirates Stadium encounter but Alex Oxlade-Chamberlain and Olivier Giroud were unable to capitalise on their clearest opening.
The Premier League men were then given an object lesson in ruthlessness from Lionel Messi, who crowned a glorious 71st-minute counter-attack before winning and converting an 83rd-minute penalty.
Speaking to BT Sport after the match, Germany centre-back Mertesacker dismissed the notion of Arsenal deserving any sympathy.
"It's tough for us now," he said. "We had to score at one point there, so that is why we do not deserve anything. You would never keep them quiet for 90 minutes, that is for sure.
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"We had a good period of time with a couple of chances and we had to score. Then we could drop back but we took more risks and they scored.
"That is why we don't deserve it because you have to score."
No side has ever progressed in a Champions League knockout tie after suffering a two-goal defeat in a home first leg, and Mertesacker is holding out little hope for the prospect of Arsenal making history.
"I think we have to concentrate on the Premier League now and I think in one month we face Barcelona with the same courage and the same bravery," he added. "We still have a little chance."
Aaron Ramsey, who nearly netted an equaliser shortly before Messi's penalty, was similarly downbeat.
"I thought, especially in the first half, we did well," he said. "We created a few opportunities and we didn't manage to take any.
"It's obviously going to be tough for us now but we will go there and try our hardest."