Should a girl 'chase' a guy she regrets losing?

I'll keep this short and sweet.
Met a guy on the internet and instantly hit it off - chatting every day for weeks. He's in the military and was away at the time, but he's based near me so when he got back we met up.
He used to ring me multiple times a week for at least an hour at a time. We only met up once but he told me he felt something, and i felt the same.
Problem is, I was a bit judgmental about some of his past (sleeping around a lot). One evening we had a disagreement about it, and the next day he blocked me on social media. We were due to meet up the next day, so i text him asking what was going on and if the meet up was still on.. he said he was fed up being judged by me so soon on and no it was off.
I didn't go OTT on texts, I apologised and said if that was his final decision i'd respect that was it.

I really liked this guy, I messed up by judging him and now he's cut me off completely. Its silly because I barely knew him, but I felt something special. He's going away tomorrow for a month with the military.

I was the last to message wishing him the best with his trip, but should I message him and ask (not beg) if we can sort it out? or should I let this one go and learn a lesson?
Should a girl 'chase' a guy she regrets losing?
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