You have to look at the context.
Barca was a laughing stock from 2000-2004.
Like Man Utd or Arsenal today. Nobody rated our players seriously because we were just bad, very bad.
Prior to Euro 2004, how Spanish football looked like?
1. Real won a Champions league in 1998, 2000 and 2002 and was named as the best team of the 20th century
They won La ligas in 2001 and 2003
2. Valencia was a CL finalist in 2000 and 2001
Winning La Liga in 2002 and in 2004 (right before Euros)
3. and then you had a club named Barca, who finished as 4th, 4th, 6th and 2nd in the last 4 years
When you take that context, Real was the best team in the world back then (something like Barca under Pep, when Spain had a lot of our players as starters, right?) and Valencia was the 2nd best team in that moment, and a team who was in form since they have just won La Liga title (the 2nd one in the last 3 years).
While we had the last title back in 99 with Van Gaal and Dutch players.
If you look at the opening match at Euros:
https://en.wikipedia.org/wiki/UEFA_Euro_2004_Group_A#Spain_vs_Russia
Real had 5 starters: Casillas, Helguera, Raul Bravo, Raul and Morientes
Valencia, the 2nd best team, had a winning midfield duo Albelda and Baraja, Lw Vicente and a defender Marchena (btw, Barca tried to buy both Albelda and Baraja for years in early 00's, especially David Albelda. He was a captain and an awesome Cdm-Cm, whom we wanted to lead our midfield)
Barca had one starter: Puyol
So, you shouldn't go too much into this why Xavi didn't played aged 24 at Euros.
Barca was horrible back then.
And Spain played with "proven" Real's players who won 3 CLs in the last few years, and with "proven" and "on fire" Valencia's midfield: Baraja, Albelda, Vicente.
Expecting Xavi to play is more or less like expecting some Spanish midfielder from Sevilla or Atletico Madrid (4th placed team) to play for Spain during Pep's era when Busi-Xavi-Iniesta (and even Fabregas) were on their prime.
Well, ok, Busi-Xavi-Iniesta were also the best, but even if there was some guy with similar abilities, you just couldn't bench them in that moment because of their club's success, momentum, chemistry together and everything.