Yes, you probably had a carp on. I’m saying this because last night I had the exact same scenario play out, except I actually got the sucker.
First time I got the fish I thought it was a huge striped bass because of how STRONG this thing fought. Just as you had, I didn’t really set the hook or anything and lost it. Literally five casts later I had the same thing out deep again! I made sure to keep constant tension on the fish, and after about a minute of the craziest fight I’ve ever felt (beating striped bass) I pulled the sucker out.
snagged the dude right on his face, really close to his eyeball but fortunately didn’t touch the eye! But yeah, it was a fun experience.