When Shanks visited Newgate, Newgate described everyone's reaction as shock. I imagine Mihawk's reaction to the news was similar to when Zoro said he defeated all the baboons. But where that realization was followed by glee, the Shanks news was probably a mixture of disappointment and sadness.
I don't think Mihawk's the type to get enraged so willy nilly. He's very "matter of fact" about things. Going back to his moment with Zoro, when Zoro first bowed to him, his feelings weren't of rage, but he was letdown and apathetic. He didn't resent Zoro, but his opinion of him lowered in that instance.
I imagine it was much the same with Shanks until Mihawk started understanding where he came from by sacrificing his arm.