Goals from Oleksandr Zinchenko and Declan Rice were enough to prevent a home defeat as Mikel Arteta made seven changes to the side which drew 1-1 with Manchester United at Old Trafford on Sunday, after a 7-1 win in Eindhoven a week earlier.
At the time of Arteta’s post-match press conference, Carlo Ancelotti’s Real Madrid side were still battling it out with local rivals Atletico but ultimately progressed after a dramatic penalty shoot-out.
Arteta said: “Well, it's obvious with the result we had from the first leg it wasn’t going to be full, but we had to continue and do the work in the manner we wanted to finish the competition.
“Unfortunately, we haven’t managed to win the game, but we decided to make a lot of rotation as well.
“You could tell in the second half we were tired; we were late to be much more dominant in the opposition half and be consistent when we didn’t have the ball.
“Overall, very happy because we are, for the second consecutive season, in the Champions League quarter-finals. We’re going to travel to Madrid.”
The Gunners have qualified for the last eight of the Champions League in back-to-back seasons for the first time in 15 years, and the Arsenal boss revelled in the prospect of taking the club deeper into the competition.
He added: “That tells you the difficulty of it. We have to value that and recognise it is very difficult to do it consistently, and now we want to make the next step, which is going to be really difficult, but we are very capable of doing it."
Spaniard Arteta also referenced the difficulties of playing against Europe’s best in the latter stages of the Champions League.
“Well, the first thing you have to be at your best when it comes to that. For the two games, for every minute, don't give anything away because they're going to take it,” he said.
“We've seen for the two goals we conceded as well. So, that's a big lesson. And again, when I decided in the boxes, when the real talent, the real performance, is crucial. And then creating an unbelievable atmosphere when we have the opportunity to play at home. That is crucial.”
The task now for Arsenal is to overcome one of Europe’s elite sides after bowing out in the quarter-finals to Bayern Munich last season.
“Well, last year we played Bayern, and with the history of those clubs and how consistent in the last 20, 25 years being there and we were right in there in the former game,” said Arteta.
“We had them under the ropes, they escaped. And when we were there, we were a bit short to get that final stage. Hopefully, we'll learn. We are better than them. And we can make it happen.”
Arsenal host Chelsea on Sunday in the Premier League, and are set to welcome Real Madrid to the Emirates for the first leg on Tuesday, April 8, before making the trip to the Bernabéu on Wednesday, April 16.