Bjørnebye's experiences as a Reds' player in the 1994–95 season under the management of Roy Evans, were markedly more successful than that of previous campaigns. He gained a regular place in the senior team, supplanting the left back position from Julian Dicks, and featured in the 2–1 win against Bolton Wanderers in the final of the 1995 League Cup Final on 2 April 1995. Subsequent injury, a broken leg sustained on 5 April 1995 in a 3–1 win match against Southampton, terminated his season and he was replaced by Steve Harkness.