Him feeling "dumb" is such an understatement of his emotional level that I think every other stone would be more 3-dimensional than the picture you're trying to build, sorry to say. I was particularly curious about his reaction, because it could be dictated by SO many things that would influence his "feelings" at this moment.
-Obito was his student and shared the same dream as him, becoming Hokage
-Obito died before Minato could get to him, I am sure he felt guilty for that, he failed him as a teacher
-By extended logic, I am sure he would feel remotely guilty for the state/person that Obito is right now, because if Minato had been there on time (or had at least tried to retrieve his body), this would have been rather avoided (or at least the shock of it). And by "this" I also mean the death of his wife.
-He would feel betrayed, because his student, whom he trusted with his life, kiiiind of destroyed his home, killed a gazillion people in the process, one of whom being Kushina, and then also killed HIM, leaving naruto alone and detested --> by extension he would feel the stirrings of revenge, although I am certain Minato would quickly rise above that.
-Despite all the shit above, he would also feel partially glad that Obito was alive after all and didn't die at such a young age
-He would feel double guilty for not saving Rin on time, which would have prevented Obito's current rage
All and all, emotional roller coaster, have fun on the Feels Ride!
