The Russian champions inflicted a first defeat on Pep Guardiola's side in Europe's top club competition in 10 matches.
Despite enjoying long periods of possession and having 13 shots on target, twice hitting the woodwork in the second half, Barca were undone by Aleksandr Ryazantsev's long-range drive and a breakaway goal from Gokdeniz Karadeniz.
"It was just absolutely rotten luck and the way the match went we did not deserve to lose," Xavi, who captained the team with Carles Puyol on the bench, told reporters.
"Rubin had two attacks and nothing more and have taken away a prize they did not deserve," the Spain international added.
"We played well but it makes it hard when your opponents only come to defend."
Barca remain top of Group F on goal difference after three of six matches, level on four points with Dynamo Kiev and Rubin. Inter Milan are bottom on three after they were held to a 2-2 home draw by Dynamo on Tuesday.
Barca next face a difficult away match against Rubin in Kazan on Nov. 4 before hosting Inter on November 24. They travel to Kiev to face Dynamo on December 9.
"It's going to be tricky but we are still top of the group and masters of our own destiny," Xavi said.
Barca's Ivory Coast midfielder Yaya Toure, who headed against a post in the fourth minute of added time on Tuesday, said the Catalans would stick to their philosophy of all-out attack despite Tuesday's loss.
"For me, Barca played a great match (on Tuesday) but the Russians are physically very strong," Toure told reporters.
"We dominated the match, but dominating is not winning," he said. "We had very bad luck."
Forward Pedro said Barca had to forget the defeat and focus now on Sunday's La Liga match at home to Real Zaragoza.
"When our next opponents come here we will be waiting for them with relish," he said.
