Despite the Spanish giants' financial problems, they spent big in the off-season and were expected to be a contender on the European stage.
However, the Blaugrana failed to get out of the group stage of the Champions League and will be competing in the Europa League after Christmas.
This is the second consecutive year Xavi's charges have been eliminated in the group stage of the Champions League, which has piled the pressure on the coach.
Many believe he has come to the end of his reign and that the La Liga outfit should move on, but Laporta remains committed to Xavi's leadership.
"Not at any point in time [has Xavi's job been under threat]. We have complete confidence in Xavi as a coach," Laporta said in an interview with Sport.
"And I can assure you that we are very proud of the coach we have. He is a coach who knows the club very well, who knows the moment at which he has arrived.
"In addition, he knows how to communicate with the different members of the club about everything that can be improved."