Rangers were knocked out of the Europa League qualifiers while Alves was on international duty with Portugal.
The 35 year old has now started training with the club and has set his sights on winning trophies at Ibrox.
"Even if we didn't play European games of course I would have joined this club," Alves said.
"It was [frustrating] because I have expectations to play European games but it was not this year.
"Maybe it is going to be next year. We need to be focused now."
Alves signed a two-year deal at Rangers after leaving Serie A side Cagliari, but was late joining up with the squad in pre-season because he was playing in the Confederations Cup in Russia with Portugal, who finished third.
Rangers defeated Progres Niederkorn 1-0 in the first-leg at Ibrox, but lost in Luxembourg 2-0 as manager Pedro Caixinha tries to blend in his summer signings - with nine players having joined the club this summer.
Alves is the most experienced, and the former Porto, Zenit St Petersburg and Fenerbahce defender is focused on helping the Ibrox club to a successful season.
"I already know how big is this club and for me I am proud to come here and join this team," he said.
"Everybody has good expectations for the season and we are working very hard to achieve what we propose to do.
"I can bring my experience and what I have learned in football.
"I have won with almost all of the clubs I have played with and I hope to bring that again to this big club.
"I am looking forward to putting the jersey on and playing and giving my best and also learn because football is continuous learning. It is going to be a good experience for myself."
Portuguese international Bruno Alves says playing European football was not a factor in his decision to move to Ibrox.