In the 285-pound heavyweight championship bracket, Cotterall was pinned by Jake Stotler of Berkeley Springs in 2:24.
Cotterall then fell into the consolation bracket and was pinned in 4:59 by Jamie Rohrbaugh of Petersburg.
Cotterall, the only Logan grappler to qualify for the state meet, had won his match on Thursday in a decision over a wrestler from Weir.
Oak Glen was closing in on its 12th consecutive Class AA-A wrestling championship on Friday.
The Golden Bears built a 40-point lead after Friday’s matches and sent four wrestlers into the finals Saturday night.
Second-place Point Pleasant has three wrestlers in the title matches. Roane County is in third place.
In Class AAA, defending champion Parkersburg advanced seven wrestlers into the title matches and has a 35-point lead over Wheeling Park. East Fairmont is third.
n The Associated Press contributed to this report