Concord managed to push the lead to 63-43 after a David Baruom putback with 6:40 left when State began its comeback.
When Juan Johnson hit his only 3-pointer of the game with 32.4 seconds remaining, State was on a 14-1 run and cut the lead to 64-57.
Concord's Paul Byrd made one of two free throws to push the lead back to eight, but after a timeout by the Mountain Lions, the Yellow Jackets turned the ball over. Concord held a 68-59 lead when Kendrick Ward banked in a 3-pointer at the buzzer to provide the final score.
Ultimately, State couldn't get much help for 6-foot-5 senior forward David Ford, the biggest concern for McBride.
Ford finished with 13 rebounds but managed just nine points on 4-of-11 shooting facing a lot of attention in the post.
"Concord tried to take away the post," Ford said. "They sagged down on us a lot. I got double-teamed a lot. But, at the same time, Anton Hutchins, Kendrick Ward and Brandon Ross, I think everybody did a good job of stepping up, but on the defensive end we just need to lock down more on the defensive end and limit teams to one shot."
Hutchins finished with 14 points to share scoring honors with Ward - two newcomers to the State program. Jordan Davis had 11 points as the only other Concord player in double figures.
However, State struggled mightily from long range, hitting only three of its 16 3-point attempts, spoiling a game in which the hosts had four more steals (12-8), four fewer turnovers (18-22) and five more blocked shots (7-2).
"We need some guard depth, but we need to execute better and not necessarily running a play, but taking care of the play and understanding what's going on in the game," Poore said. "When to drive and when not to drive, when to pass and when to shoot. We're not playing with a purpose. We're just kind of out there balling. Our there balling in this league don't get it."
State hosts Wheeling Jesuit on Saturday before Tuesday's visit to West Liberty, the No. 1 team in the National Association of Basketball Coaches NCAA Division II Poll.