The Quakers (2-10) played their second consecutive game without junior forward Fran Dougherty, who averages a team-high 15 points and nearly nine rebounds per game, but is suffering from mononucleosis.
Penn countered by making 53 percent of its three-point attempts, led by Miles Cartwright, who had three and finished with a team-high 15 points. Freshman Tony Hicks added 10 points off the bench.
Hicks hit a three-pointer that cut Butler's lead to 52-49 with just under 10 minutes remaining. Butler immediately answered with a 10-0 run that was ignited by starting sophomore forward Roosevelt Jones, who scored six of his career-high 24 points during the stretch.
Jones entered the game averaging 8.3 points and was Butler's fifth-leading scorer. He shot 10 of 15 from the field against Penn.
"I don't think he took one jump shot," Allen said. "He did a good job of being physical and picking his spots."
The Quakers got no closer than eight points the remainder of the game. Allen lamented some quick shots by his team that helped fuel Butler's decisive run.
Butler's other starting forward, Khyle Marshall, added 14 points as he and Jones combined to shoot 17-for-25 from the field.
"I thought we won the game with power and our interior guys," Butler coach Brad Stevens said.
The Bulldogs had to win the game inside because they were off from the perimeter, shooting 4-for-19 from the three-point line.
Butler senior Rotnei Clarke, who came in averaging an NCAA-leading 4.1 three-pointers made per game, was limited to six points and went 1-for-9 from beyond the arc.
Penn committed 19 turnovers, with 11 in the first half. Throw in the rebounding problems and Allen had all the stats he needed to explain the loss.
"[Butler] is an extremely good team because they play hard and don't beat themselves," Allen said. " . . . With 19 turnovers and giving up 13 offensive rebounds, you're not going to win many games in Division I college basketball."