Barca's frustration was amplified in stoppage time when Sergio Busquets was shown a second yellow card for what deemed an elbow to the face of Rayo striker Falcao.
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Barcelona began with three of their summer signings -- Robert Lewandowski, Raphinha and Andreas Christensen -- in the starting lineup after they were finally able to be registered with LaLiga on Friday night. But Xavi Hernandez's side, seeking to win the Spanish title for the first time since 2019, could not find their way through an impressive performance from last season's 12th-placed team.
"I understand the disappointment, expectations are really high," Xavi said. "We will have to analyse the game, improve and keep believing in the model of play. Rayo defended well. It was harder for us to create [chances] than usual. It's a shame because we wanted to show the fans that we're on a good path. It's disappointing, but we ask for patience."
Lewandowski had the ball in the net just 12 minutes into his Barcelona debut but the former Bayern Munich striker's well-taken effort was correctly ruled out for offside. Another of the new signings, Raphinha, then had Barcelona's clearest chance of the first half to break the deadlock. From Ousmane Dembele's cutback, the former Leeds United attacker shot high over the crossbar as he leaned back on the shot.
As Barcelona struggled to break down Rayo, the visitors were not without an attacking threat of their own on the break. And Marc-Andre ter Stegen was twice forced into crucial interventions either side of half-time to prevent his team falling behind. First he stood up to block well from Alvaro Garcia and then closed down Sergio Camello after the Rayo forward twisted his way into a clear scoring opportunity.
Almost immediately Ansu had a chance to break the deadlock but his first-time shot was parried away by the impressive Stole Dimitrievski.
More chances were forthcoming for Barca as they finally showed some urgency in the final minutes, but both Lewandowski and substitute Pierre-Emerick Aubameyang were unable to take advantage.
Both teams also had the ball in the net late on before the offside flag was rightly raised as Barca finished with 10 men and dropped two early points in their attempts to overhaul defending champions Real Madrid.