Villa were thumped 3-0 by Palace on Saturday, with Ismaila Sarr scoring twice and Ebere Eze also on the scoresheet.
"I’m sorry for our supporters,” he said. “We were very motivated and we wanted to share our moment with them here in the semi-final. We have to accept how we lost this match, because Crystal Palace played very well and we didn’t perform like we are usually doing.
“How we are increasing our level and our demands through Europe, in the Conference League last year and Champions League and FA Cup this year, we have to be happy, motivated and excited about how we are improving and increasing so quickly the process we are doing here.
“In some matches like today, when we’re being disappointed and frustrated, we have to dominate our frustration and disappointed moments and keep going.
“We have to change again our objective because the Premier League is our priority. Through it we can again play in Europe next year."
"We have to keep going"
Emery sought to rally the players and the fans after the Wembley defeat, with a European place in the Premier League still available.
He continued: “We lost a possibility to get one trophy in the Champions League and again today, but we have to keep going. Only one team is winning, and to play in Europe consistently is the next objective and the priority when I arrived here.
“This is the message I send always to the supporters: to be consistent in Europe, to try to play for a trophy - we did this year and last year we did as well in the Conference League.
“We keep going and we really need next week against Fulham at home every supporter trying to be close to us, supporting us and helping us to get again our full energy to play the final four matches.
“It’s our objective to play again in Europe.”