Gerard Pique's 28th-minute header was all that separated the Group F opponents as new boss Luis Enrique enjoyed a winning debut in Europe at the Camp Nou.
Wednesday's victory ensured Barca's solid start to the season continued, with the Spanish giants having won all four games they have played so far without conceding a goal.
Barca, however, did not have it all their own way on Tuesday as a resilient APOEL provided a tougher-than-expected test, and Xavi was satisfied with the hard-earned win.
"We were made to suffer. We couldn't find the usual fluidity in our play and it was difficult for us. They played very well defensively," said the 34-year-old.
"When things aren't going your way and you keep missing chances, your opponents grow in confidence and in the end it was a difficult game for us.
"But we got the three points that we needed. I'm very happy to have started the game."
Barca and Spain legend Xavi was handed his first start of the season, having been named among the substitutes for his club's opening three La Liga matches.
The Spaniard lasted 61 minutes before being replaced by Andres Iniesta on a night that also saw Luis Enrique hand Champions League debuts to Marc-Andre ter Stegen, Sergi Samper, Sandro Ramirez and Munir El Haddadi.
And Xavi added that he is ready to play whenever he is called upon by the coach.
"I want to enjoy all the minutes I get to play, do a good job and I'm available for whenever the coach needs me," he continued.
"I will try and have as big a role as possible in the team. Players such as Sandro, Munir and Samper have a lot of talent and are lucky to have a coach who trusts in them.
"Luis Enrique is a very brave coach."