Vronsky feels humiliated. According to the rules by which he leads his life, the cuckolded husband is a pathetic creature, but Karenin has acted nobly and with dignity. Vronsky feels that he has been made ridiculous, and yet he is more in love with Anna than ever.
Karenin doesn’t act in accordance with the way Vronsky sees the world, which forces Vronsky to recalculate his entire world view: if Karenin has dignity still, what does that make Vronsky?
When Vronsky goes home, he is unable to sleep; events with Anna and his humiliation turn around and around in his mind. Vronsky picks up a loaded revolver, holds it his chest, and pulls the trigger; he wounds himself but fails in his effort to kill himself.
When Karenin, not Vronsky, seems to be the hero of the situation, Vronsky feels he has nothing left to live for, but unlike Anna, who eventually succeeds in her suicide, the suggestions here is that Vronsky does not have passionate enough emotions to carry the deed to fruition.