Born in Hillerød, Budtz became an instant hero in his first game for Doncaster Rovers when he replaced the injured Andy Warrington during a League Cup tie against Manchester City in September 2005. He saved two of the three penalties taken by the Premier League side during the shootout to send Doncaster into the next round (the first penalty, by Darius Vassell, hit the crossbar). His name was subsequently plastered all over local and national newspapers the following day and he also made several appearances on local TV news channels.