Unlucky indeed became one of the factors why we did not see Barcelona in the round of 16, also indeed their game in the Champions League was not more promising when they played in La Liga matches. Maybe this happened because in the Champions League the team they faced had a better mentality than the team in La Liga. We'll see how they were beaten by Inter Milan and also Bayern Munich, 2 teams from Serie A and the Bundesliga.
I don't think they only focus on La Liga and that's why they aren't optimal in the Champions League. I agree with what you said that these two titles are the prestigious titles they definitely want. But for the Champions League they have to be more patient and wait until their situation is more stable and solid after going through several problems from the previous season.
If we talk unlucky, Barcelona is less fortunate from the factor of the players getting injured. in particular, the two Barcelona defenders. the rest, purely Xavi's strategic mistakes and the poor performance of his players. moreover, if you look at the roles of Busquet and Pique, who made several blunders.
Xavi is too confident with the same strategy, he rarely even experiments with rotating his players. Xavi has always prioritized La Masia players to be the main straters, Gavi and Pedri, De Jong who is more experienced is always placed as a substitute player. on the wing, Raphinha did not contribute at all to the Champions League, but Xavi remains confident in his plans and strategies, even though Barcelona have the option to play Ansu Fati.
in the end, Xavi realized that the strategy he was implementing was not working effectively in the champions league. then he tried to rotate players, but unfortunately he realized it too late. Barcelona has a good depth of players, but it's a shame Xavi can't optimize his players. at least, Barcelona needs time to become strong so that they are on par with other big teams competing in the champions league.