The Blaugrana go to Seville on Sunday (AEST) sitting second in LaLiga, eight points clear of fifth-placed Betis, which won 1-0 at Camp Nou in December, as the battle for the top four nears its conclusion.
A win for Barca over the Copa del Rey winner would take it to 69 points and ensure it does not finish any lower than fourth, with Betis only able to reach 67 and sixth-placed Real Sociedad 68.
While the 15-point gap to champion Real Madrid highlights how confronting 2021-2022 has been for Barca, Xavi has restored a degree of positivity since replacing Ronald Koeman in November.
Barca was ninth in LaLiga after 13 matches ahead of Xavi's first game in charge, 10 points behind second-placed Sevilla; it now appears favourite to finish ahead of Julen Lopetegui's side and dethroned champion Atletico Madrid as runner-up.
Xavi wants his team to clinch UEFA Champions League qualification at the first time of asking.
"Hopefully, it's a golden opportunity to qualify for the Champions League," he said. "They're a direct rival, with great players and a great coach. It will be difficult.
"Football gives us the chance to take sporting revenge. We want to fulfil our goals before the end of the season.
"We are fighting for the minimum, but that's the way it is. There are two goals, but the most important is to be in the [UEFA] Champions League next season.
"That's the objective. If we can get second, which would give us the option of entering the Supercopa, then even better.
"We cannot think beyond this, [but] I hope that this summer there will be signings despite the economic situation. We cannot take the European qualification for granted.
"I expect an opponent [Betis] with a lot of confidence. They have won the Copa [del Rey], they deserved it. I congratulate Betis, [Manuel] Pellegrini and the players, who are having an excellent, historic season. I congratulate them."
Ever since Xavi's return to the club, its "philosophy" and "DNA" have drawn a lot of focus, with many supporters feeling Barca's ethos was diluted under Ernesto Valverde, Quique Setien and Koeman.
Ronald Araujo commented that restoring "the Barca DNA" with Xavi was a chief goal of his after signing a new contract in April, and while the coach acknowledges he cannot change things in an instant, he is confident it is making progress with a top-four finish almost secure.
"It's not my message, it's the message of Barca's history," Xavi continued. "I don't have a magic wand, what I'm clear about is that with this model [Barca] won five Champions Leagues and world recognition.
"You leave Spain and they remember [Pep] Guardiola's Barca, [Lionel] Messi's Barca, and they remember how we won, not so much what we won.
"We have to wait and be patient. If we review history, there is no doubt."