Unai Emery's men secured their spot in the next round of the competition with a 3-0 home win against Rennes on Thursday night, thanks to a Pierre-Emerick Aubameyang double and an Ainsley Maitland-Niles header.
The Gunners left themselves with a mountain to climb at the Emirates Stadium after losing 3-1 in the first leg in France, failing to learn their lesson after an away loss in the round of 32.
BATE Borisov beat Arsenal 1-0 in Belarus before the Premier League giants once again managed to turn things around at home with a 3-0 triumph.
The draw for the Europa League quarter-finals was completed on Friday, with Arsenal handed a tough draw against Serie A powerhouses Napoli.
The first leg is set to take place at the Emirates on April 11, and Kolasinac has insisted that the Gunners must avoid another damaging defeat.
“It’s always very difficult when you lose the first game,” the 25-year-old stated post-match.
“We are aware of that, it’s not something we want to do of course. It is something we are going to work on in the next round. Of course, the key will be to start better than we have in these last two ties.
“We didn’t put ourselves in a good position at the end of that first leg. Having said that, I think that away goal was crucial for us.
“It was difficult for us because we had to play with 10 men for about 50 minutes of that first game as well. We made it difficult, but we knew how strong we are at home and we deservedly went through tonight.”
Arsenal join Chelsea in the latter stages of the Europa League, while Manchester United, Tottenham, Manchester City and Liverpool have also progressed to the quarter-finals of the Champions League.
Kolasinac believes the success of English sides in Europe's top competitions proves the Premier League is the strongest in the world, as he added: "I think it characterises us and it characterises this league at the moment as well that all six teams have got through to the quarter-finals,” he added.
“It proves that when people say the Premier League is the best league around, they are not saying it for free. I think it makes the Premier League very interesting and we’re of course proud to have progressed in the Europa League.”
Emery's side can now enjoy a well-earned break while the latest round of international fixtures takes place, with a crucial clash against Newcastle up next on April 1.