The Gunners, after winning 1-0 thanks to Kai Havertz's injury-time goal, reached the final 4-2 on aggregate.
"It’s disappointing not to get to the final," Chalobah said afterwards. "It was a chance for us to get to another final and win another trophy, but it was just the final details in the attacking third.
"I thought there wasn’t much in the game, and we did really well to nullify them, especially in the first half.
"They had a chance at the end, but the boys did well – it was just the final details. We stuck to the game plan. We were pushing at the end, but it didn’t work out. We have to keep our heads up and not allow this to affect us and carry on our good form."
He continued: "Arsenal didn’t create many chances, they didn’t really hurt us in that final part of the game, it was just the final details – finishing our attacks or getting shots off, and for us that’s what we need to improve.
"We needed to get more shots off, but it’s hard to break down Arsenal and their defence – it’s something we can learn from. We can keep our heads high and move on to the next."