I don't think so. "Heat of the moment" - sure. "Rush of blood" - sure. That suggests your judgement is clouded by emotion or that you were blinded by only thinking about the ball and not the opposition at all. To be fair, this may have been the case - I don't know what was going through Ramsey's head, but like yourself, I can only assume.
Genuinely thinking you're doing what is right? No, that's not reckless. You can't define inaccuracy as recklessness in a sport like this. I wouldn't say that when a ref incorrectly believes a player didn't intentionally handball that the ref is being "reckless", I'd say he got it wrong. I wouldn't say that a player going for a header and not getting it is reckless, I'd say he missed. It's not Shawcross's fault that he didn't think Ramsey was going to get the ball, nor is it his fault that Ramsey's leg was at the exact right spot for connection at the time. At that speed, Shawcross could (I won't say 'did' because I won't pretend to know for certain, but I mean, nobody does) easily have believed that he was going to connect with the ball and that Ramsey wasn't going to get it, and that he was not going to connect with Ramsey in any way. He was running at a high speed, he made a judgement call, a snap decision, that he could get this, that he was going to beat Ramsey to it.
He was wrong. Reckless is slamming into the player with your body, as that is careless, unconcerned about the consequences, without caution, without care of danger. Instead, Shawcross went for the ball. He could have easily done the reckless thing and got the same end result - breaking up the play. But instead he went for the way which he believed would minimise damage potential (and you can never completely minimise potential damage without, as you said, making it a non-contact sport).
Wrong != Reckless.