Barca were poised to reach the semi-finals following last week's 4-1 rout at Camp Nou, however, the unbeaten La Liga leaders were stunned 3-0 by Roma in the Italian capital Tuesday.
Goals from Edin Dzeko, Daniele De Rossi and Kostas Manolas sealed one of the greatest European comebacks on away goals as Barca were beaten in the knockout round after winning the first leg by at least three goals for the first time in its illustrious history.
Reflecting afterwards, Spain international midfielder Busquets told reporters: "Probably [the worst defeat of my career] because the way it was, and the result we had in the first game, with a good season we are having.
"But in the end, the important thing is game by game. We come from a good season, from a good dynamic but unfortunately today it has been cut short, and this is the end of our way in Champions League."
"It's very difficult to be honest," Busquets added. "A sad night, one to forget. They beat us in all the ways, they took us where they wanted because they needed a big result, and unfortunately they got it."
Barca are back in action in La Liga at the weekend, with the Catalans set to face off with Valencia on Saturday.