He had just Devil Triggerd for the first time, he had unlocked his inner devil. That's why he got stronger then beforeThe writers seem pretty selective when he can feel pain, and when he can't. On one hand, he can be stabbed in the heart with Rebellion and be shot in the face by Lady without so much as wincing or cringing in pain.
And even when he does feel pain, there's no weight to it. He's up and about in only a few seconds---without a stagger in his step, or even a hindrance to his physical performance. The only instance where showed any kind of strain was when he got up after first fighting Vergil, and even then, he dove into an extravaganza of over-powered acrobatics and skill like he hadn't even taken a scratch.
If Dante can feel pain---and there's not a consistent basis to determine whether or not he actually can, especially since the extent of his powers, limitations and weaknesses are never given over the course of four games and multiple media spin-offs---he sure has hell doesn't have to endure the traumatic or taxing effects of it. Why? Because that would actually weaken him as a character---and God knows we can't have Dante not be an overpowered Gary Stu for more than three seconds.
We wouldn't know if Dante would've lost the fight or not, or if the exhaustion would've amounted to anything because Dante would never lose that fight....because he wins practically every fight.
Dante's never experienced the struggle of a personal defeat, and won't ever be shown enduring any kind of actual pain. A character's feats of strength are only impressive if he performs them in the face of certain vulnerabilities or weaknesses...overcoming any possible barriers of strength, or shortcomings they may have. It's something that causes them to work harder, to train harder...to bypass the limitations over a span of time, and prepare themselves for the heat of the next battle.
But Dante just ends up winning 99% of every fight he's dealt with, and whatever pain he feels is showered upon him without any real consequence. He has no limitations, no logical or anatomical fallacies, and no danger of being defeated or killed...
....thus making every battle a cakewalk instead of a real obstacle. And that just makes him a weak character...the kind of Gary-Stu that Deviantartists cook up on an afternoon of eating sugar and watching devoid-of-logic hyper bishonen.
Tell that to Alucard