Xavi felt Barcelona "deserved more" from Thursday's defeat at Manchester United after Antony's 73rd-minute strike dumped his team out of the Europa League at Old Trafford.
Following a thrilling 2-2 draw at Camp Nou last week, Robert Lewandowski converted a penalty after Bruno Fernandes hauled down Alejandro Balde to put Barca ahead at half-time of the second leg.
But Fred equalised shortly after the interval, and Antony struck with less than 20 minutes to play to send United through 4-3 on aggregate and knock Xavi's side out of the competition.
It was Barca's first defeat against the Red Devils since 2008, and the first time in 38 matches in all competitions that they had lost a game after leading at half-time.
Xavi believes his players' efforts at Old Trafford warranted more than they received, telling Movistar+ after the match: "In such evenly matched knockout matches, details are important. I think we deserved something more.
"The goal to make it 1-1 hurt us. We lost a ball and they equalised. They put more intensity and we lost more duels in the second half.
"It has been an even tie. There have even been moments in which we have been very comfortable.
"This is a big disappointment but we have to focus on the competitions we have left. We had a great rival in front of us."
1 - #Barcelona have just won one of their last 15 games in Europe against teams from the top 5 European leagues (D5 L9), as many defeats as in their 50 previous such games (W31 D10 L9). Fall. pic.twitter.com/6BCmCIBpYM— OptaJose (@OptaJose) February 23, 2023
Despite Barca having now been knocked out of both the Europa League and Champions League this season, Xavi says this season's continental efforts have been an improvement on last campaign, when they were again knocked out of Europe's premier competition before succumbing to Eintracht Frankfurt in the Europa League final eight.
"We have been better than last year," Xavi explained. "The message is a bit like when they eliminated us in the Champions League. This year we have competed against Bayern [Munich], against Inter.
"We have been better. We have competed in this tie.
"You have to be very self-critical and think about what needs to be improved. We may not be satisfied, but there has been an exponential change compared to last year.
"Next year we have to improve. They are big teams and it is hard to compete. Next year we will come back stronger."
Asked whether new signings are needed for Barca to compete at the top level again, Xavi replied: "Soon we'll see if we can sign [players]. What is clear is that we haven't competed for two years."