Dortmund finished on top of Group F after Kevin Grosskreutz scored an 87th-minute winner in France on Wednesday.
The result meant that Napoli - who, like Dortmund and runners-up Arsenal, finished on 12 points - missed out, although things looked like being very different in the dying stages.
With Dortmund still level against Marseille, last season's Champions League finalists were set to depart the group, only for Grosskreutz's late intervention.
"Perhaps we pulled off the impossible," Mkhitaryan said.
"We're very proud. We played a great game and, although we didn't score all our chances, we managed to score a second goal. That's what matters because during the game we heard that Napoli were winning 1-0, so we gave all we had on the pitch to get over the line.
"We could have ended up first or third in the group, but we did our job well and took first place.
"It was important to finish top because Dortmund were finalists in this competition last year. This year it was a tough group; it was a tough group last year as well, but maybe there were people who doubted that we could finish top or even second this time.
"(After the winning goal) I remember feeling happy because there were just four minutes to go.
"I'm very proud we got it because throughout the group stage we've had problems, with red cards, injuries and so on. In spite of that, we still had players who could come in and play a great game."
The win brought back memories of Dortmund's last-gasp quarter-final win over Malaga last season, in which they scored twice in stoppage time of the second leg to claim a dramatic 3-2 aggregate triumph.
Goalkeeper Roman Weidenfeller said his side have the belief they can win matches right up until the last kick.
"We heard about the score in the Napoli game and two minutes before the end we were out," he stated.
"Then, moments later, we were first in group. We're very happy to have made it and it was a very tough group. It was like against Malaga last year, when we knew we would score a goal."
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