The Blues speedster was disgruntled after starting as the team's substitute, and was consequently dropped from the side for Friday night’s clash with Hawthorn.
When addressing the president's function on Friday night, Kernahan said Yarran's omission was a "statement" as the club tries to improve its culture.
"Chris has worked harder than anyone else on the track this week," Kernahan said.
"The club demands a level of excellence. He didn't meet that last Friday night, and he's paid the price. I think it's fair to say the coach has made a pretty strong statement.
"We'd love to have 'Yaz' out there today, because it suits him beautifully the fast track, but we're trying to get this club up and going and it wasn't acceptable what happened last week. Disappointing."
Coach Mick Malthouse is confident Yarran has learnt his lesson.
"Chris is the first to realise, and has said that he wasn't fully switched on once he'd been told that he was the sub, and as a consequence, it affected him and it affected his teammates," Malthouse told SEN Radio.
"It certainly affected the bench.
"When I said to him that he won't be playing this week, he was all over it. He said, 'I totally understand and expected that'.
"We've got a side that we're trying to create a culture that is built on excellence, built on effort, built on teamwork. All those players that have been less than that understand it.
"We're trying to get that right, and the only way to get that right is to be hard."
Jacqui Reed is a reporter at AFL Media. Follow her on Twitter @JacquiReedAFL
