The Gunners won 1-0 thanks to Kai Havertz's injury-time strike, with Arsenal reaching the final 4-2 on aggregate.
Rosenior said, "We dominated the areas we wanted to in the second half, but we didn't find that quality moment.
"When you're pushing as we were, we put both defenders in the box and in the last few minutes of injury time that (conceding) can always happen.
"Arsenal know they were in for a game today, over both ties. I think there are clear improvements from the first leg to the second. Yes, it's painful to lose - you want to go through. We just need to keep making improvements - which I'm seeing."
Asked about regrets from the first leg, Rosenior also stated: "In the first leg, I'm not making excuses, but we had an illness go through the camp on the day of the game - we had four players missing - and I'd been in charge for three days. I cannot fault the application, intensity or the fight of the players.
"What we need to do is remember this is the start and I'm really, really happy with a lot of things I'm seeing. You want to get the results - but we need to make sure we rest and recover and we keep improving as we go."