The loss sends them tumbling out European football's Champions League at the last-16 stage for the seventh season in a row.
Wenger is under increasing pressure to leave Arsenal after more than 20 years in charge.
They have not won the Premier League title since 2004 and the Frenchman felt his side should have been awarded a penalty in the first half.
"It's definitely a penalty on Theo Walcott, Lewandowski is offside and after the red card it was very difficult for us to finish the game," he said.
"My team has produced a huge effort tonight and played very well."
Former Arsenal striker Ian Wright believes Wenger's long reign at the London club is nearly over.
"It's a sad day because we've gone out again at this stage. We're going through a period in our history that's the worst," Wright said.
"With everything that's going on you have to say it will take some sort of monumental effort for Arsenal to turn it around in terms of the drive and determination of the players," Wright added.
"It feels like something is coming to an end."
Before the match about 200 Arsenal supporters held a protest march against Wenger.
Fans organised a march from the club's former Highbury home to outside of Emirates Stadium where protesters held aloft banners calling for Wenger to leave and for the club not to offer the 67-year-old a new contract, with his current deal expires at the end of the season.
As well as their anti-Wenger signs, there were plenty of chants aimed at the manager and the board.
"We want Wenger out," was the most popular chorus among the disgruntled numbers, while chief executive Ivan Gazidis was also targeted with chants of "Ivan, do your job".
The march ended on the steps of the 60,000-capacity stadium which will be part of Wenger's legacy at Arsenal following a reign of over 20 years.
The defending champions Real Madrid moved into their seventh straight quarter-finals with a 3-1 win over Napoli giving them a 6-2 aggregate score.