Quick played collegiate hockey for the University of Massachusetts Amherst out of Hockey East (HE). As a freshman, he earned his first victory by a score of 4–2 on October 15, 2005, in his first start against Clarkson University. He also appeared in one playoff game as a freshman, which the Minutemen lost 4–1 to Boston University. Quick scored his first goal January 6, 2007, against Merrimack College. In the 4–2 win, the unassisted goal came during a delayed penalty into an empty net at 9:31 of the second period; it was the game-winning goal. While playing for the Minutemen, he led the team to their first-ever NCAA Men's Ice Hockey Championship appearance. In his first NCAA Tournament game, Quick shut-out Clarkson University, stopping all 33 shots he faced, in a 1–0 overtime victory. He appeared in five playoff games and posted a . 944 save percentage.