The 6-foot-6, 285-pound Crick made 22 tackles, including three for loss, in an injury-shortened 2011 season. He finished in Nebraska's top in career sacks (20), even after tearing a chest muscle in the sixth game of his final year.
Earlier in the fourth round, Houston selected Georgia center Ben Jones (99th overall) and Michigan State receiver Keshawn Martin (121st overall).
The 6-foot-2, 303-pound Jones will back up Chris Myers, who made his first Pro Bowl last year and signed a four-year deal in free agency. The 5-foot-11, 181-pound Martin was an honorable mention All-Big Ten selection after ranking second on the Spartans in receptions (66) and yards receiving (777) in 2011.