Koenig scored 14 points to lead all scorers during the Badgers' scrimmage at the Kohl Center, but the junior point guard was one of several players who struggled to put the ball in the basket.
Nigel Hayes made a 3-pointer in the final seconds to lift the Red team to a 47-45 victory. Hayes missed his first eight shots before connecting twice from beyond the arc in the final 97 seconds.
The teams combined to shoot 40.2 percent overall and 27.3 percent from 3-point range, but Wisconsin coach Bo Ryan said he wasn't concerned by those numbers.
''We've shot it better than that (in practice),'' Ryan said. ''I think we forced a few shots. The guys know they're only going to play `X' number of minutes because you've got to get eight, nine guys in there. So some of the shots were forced, which obviously gives you a low shooting percentage because they're not the best shots.''
Wisconsin is in the process of replacing five key players from a team that went to back-to-back Final Fours and lost to Duke in the NCAA tournament title game last season.
The Badgers shot 47.9 percent last season - the best mark in Ryan's 14 seasons with the program - behind national player of the year Frank Kaminsky.
Wisconsin returns two proven scorers in Koenig and Hayes, but the two stars combined for eight turnovers and 17 missed shots in the scrimmage.
Koenig believes Wisconsin's offense will be just fine once a young roster gains more experience.
''I know guys will step up for us,'' Koenig said. ''That's going to be a big part of our offense is drive and kicks and stuff like that, because we have quick guards who can penetrate and get in the lane.''