The Gunners hold a 3-2 aggregate lead, though Alejandro Garnacho's late second goal offers the Blues hope of turning things around at the Emirates.
"It's half-time," said Rosenior. "I was very happy with the engagement, the commitment of the players. They gave everything. It was every open game. Disappointed to concede from a corner. Disappointed with the third goal as well because we were right back in the game and we were on top at that moment.
"We switched off from a restart from a central free kick but I can't fault the players. We've had illness in the squad, we've picked up a few knocks this week but what the squad has shown that they are willing to run and fight for each other."
On goalkeeper Robert Sanchez conceding three times, Rosenior said: "Rob's a very good goalkeeper. He made an outstanding save at 3-1 to keep us in the tie, so for me load of things to improve but the overall attitude of the team I liked. Hopefully, we get a few bodies back for Brentford on Saturday."
And on Garnacho coming off the bench to score twice, he concluded: "I said he would be important off the bench and he proved that today. I've got an outstanding squad.
"What I need them to do is be engaged whether they start the game or whether they come off the bench. Garna showed his quality. I think Pedro Neto was magnificent. Estevao was outstanding as well.
"We need to make sure i we perform well individually we don't concede as many goals."