The Flyers, who improved to 3-1, did much of their damage at the free throw line, hitting 27-36 foul shots to provide the winning margin. Auburn was 13-17 at the foul line.
Dayton's top scorer in the game, senior guard Kevin Dillard, scored 12 of his 20 points at the foul line.
Barbee said his team's lack of toughness was its downfall vs. the Flyers. "Right now it is nowhere near where it needs to be," he said. "We got out-toughed by Murray State and we got out-toughed by Dayton, and when I looked back at the tape we got out-toughed by College of Charleston."
Sullivan agreed with his coach's assessment of how the Tigers lost on Sunday at TD Arena. "In the two games we lost this year, that's where we lost it," the senior guard said. "It is toughness and rebounding. We got outrebounded and we got out-toughed in this game, and we need to come out against Boston College and play the way we know how to."
The game was close for most of the first half, but the Flyers made a 13-2 run to close the period and turn a 23-22 Auburn lead into a 35-25 advantage at intermission.
Barbee said that stretch in the closing minutes of the first half was the big difference in the game along with his team not being able to make open shots while trying to come back in the second half.
"I thought we got great looks," he said. "We got open threes, post-ups close to the rim and offensive rebounds close to the rim," he said. "We got layups in breakdown situations."
Dayton built its first half lead at the foul line by hitting 13-16 free throws while Auburn made just 1-2 foul shots in The Opening half. The Tigers hit 11-26 field goals in the first half while Dayton made 10-26.
Auburn hurt its cause with 10 first half turnovers, four more than Dayton, which held an 18-17 rebounding edge at the break.
The Tigers cut the lead to 38-32 early in the second half on a three-pointer by Allen Payne, but could get no closer the rest of the way.
"We have got some guys who are tough, but unfortunately right now we have got the majority of our team that is not," Barbee said. "That is all I preach, that is all I talk about, that is all we work on--being mean, nasty and tough the entire time you get on the floor. We are not physically tough and we are not mentally tough either."
Frankie Sullivan led all scorers despite playing with 25 stitches in his shooting arm from an injury he received diving head first for a losse ball vs. Murray State.
Sullivan scored his 23 points by hitting 6-15 field goals and making 10-11 free throws. He added five assists and turned the ball over just twice.
Rob Chubb scored 11 points as made hit 5-10 field goals. He added five rebounds.
Noel Johnson came off the bench to score 10 points. He hit 4-7 field goals and was 2-3 on treys. Payne added nine points and four rebounds.
The Flyers won the rebounding battle 33-27, but had 17 turnovers, three more than the Tigers.
"They were tough on every catch," Barbee said of the Flyers. "They were tough on every drive. They were tough on every post up, and we weren't. That is the bottom line in this game.
"That is why we got so many balls knocked out of our hands, balls that just slipped out of our hands while we fumbled so many rebounds," he added. "It is all about our level of toughness which is almost non-existent."
Final Numbers: Auburn hit 41.8 percent of its field goals, making 23-55. Dayton hit 46.7 percent (21-45) from the field. Each team made four treys. Dayton tried 13, Auburn put up 16.
Tigers vs. Flyers: Sunday's game was the fourth all-time matching Auburn vs. Dayton. The Flyers won the previous three matchups. Auburn dropped to 26-13 all-time vs. Atlantic 10 teams
Up Next: The Tigers will travel to Boston College for a 3 p.m. CST tipoff on Wednesday in Chestnut, Hill, Mass.