Abrecht began attending Princeton University in the fall of 1982. The Tigers weren't very good in those years but, despite the team's lack of success, Abrecht played well enough to get selected in the NHL Draft. He was a solid player for Princeton over his first three seasons but Abrecht had a tremendous finale. While serving as team captain, Abrecht set new program records for defensemen with 15 goals, 26 assists and 41 points. He also became the program's all-time leader for goals, assists and points by a defenseman (he was surpassed in assists in 2019). He did all of that in just 30 games and was named an All-American, the first for the program in 33 years. However, because the Tiger's finished 9th in the ECAC Hockey standings, they weren't even allowed to participate in the conference tournament. Abrecht signed with the Toronto Maple Leafs after the season, playing 1 game for the St. Catharines Saints.