Stoops had been critical in the past of shared championships, but changed his tune late last season when it appeared the co-championship with Kansas State might happen.
The Oklahoma players' tweets were reminiscent of May 2011, when former Oklahoma State quarterback Brandon Weeden tweeted a photo of his 2010 Big 12 South Division championship ring.
OSU, OU and Texas A&M shared the division title, but the Sooners advanced to the Big 12 championship game because of the BCS standings.
“Love how @bweeden3 posted that pic of Big 12 ring,” former OU safety Tony Jefferson tweeted then. “Didnt win that bud. #sorrypokes.”