The result means Arsenal remain without a trophy since 2020.
“It’s very, very disappointing,” Rice said afterwards, “very tough. It's a final you didn't want to lose but ultimately today we’ve given them the two chances. We've got to look at ourselves, it could’ve been a different game if we scored that one in the first half. There were a lot of positives in the first half. But look, we keep going. A lot of positives to still look forward for the end of the season.
“I know how much it meant to the Arsenal fans today, you could sense that. But still now, we have three big competitions to play in. We need to stay positive, stick together and keep going because there's a lot to play for.
“Top of the Premier League, still in the FA Cup, the Champions League. We could have been better today on the day but that's football. Now there's still so much to look forward to over the next two months. So we keep going, keep fighting for the badge, for the fans and there's still so much to play for.
“I saw the fans today, how much it meant before the game, them singing for us - I was proud today to be an Arsenal player. You could see how much it meant to them to be in the crowd, to come out and support in their numbers across the city, to come here today. Obviously, we're gutted that we let them down because they deserve something.
"They've been with us home and away all season. They never give up, they're always with us. Like I said, it's disappointing we haven't won this one. But hopefully, there’s a couple of competitions that we're able to do well in still.”