In a tight, tactical contest, United had early possession but were kept at bay by a disciplined Palace side and several key saves from Lucca Benetton. After a goalless first half, United led through JJ Gabriel in the 76th minute before Raihaan Anderson quickly equalised following a goalkeeping error.
With chances at both ends in extra time, Donte Martin and Kairo Smith-Phillips went close, but Obi struck late to settle the tie.
On the performance, Alonso said: “I’m really proud of the fight of the boys. They ran a lot, they pushed themselves a lot. I can’t say anything bad about them because they gave their best. In this stadium, against one of the best teams in the country – we are as well – I’m really proud. We played two hours.
“The performance was really good. The first half was more for them, but we improved massively in the second half and had chances between the 80th and 90th minute to win it.”
On emotional control, after focusing all week on staying composed, he added: “We started a little nervous, which is normal in a big occasion, but we improved massively during the game, playing more calmly and switching the ball better.
“We spoke at half-time and the second half was much better – we just didn’t take our chances.”