Lee was chosen with the 39th overall pick.
"A sense of relief but then it's motivation at the same time," Lee told the NFL Network.
Lee joins a Jacksonville team that selected quarterback Blake Bortles in the first round.
Lee, the 2012 Biletnikoff Award winner as college football’s top receiver, was projected by many as a first-round pick.
But he was not among five receivers selected in the first round Thursday.
Clemson receiver Sammy Watkins was chosen fourth by the Buffalo Bills, Texas A&M’s Mike Evans seventh by the Tampa Bay Buccaneers, Louisiana State's Odell Beckham Jr. 12th by the New York Giants, Oregon State’s Brandin Cooks 20th by the New Orleans Saints and Florida State’s Kelvin Benjamin 28th by the Carolina Panthers.
Lee caught a school-record 118 passes in 2012, but he had only 57 receptions during an injury-plagued 2013 season, perhaps the most tumultuous in USC history.