New in my job, made a mistake with crediting a colleague – how should I handle this?

I did about 90% of the work myself... I asked a colleague to review it... [and] he dropped by spontaneously and gave me some quick feedback in about 20 minutes... overall his contribution was pretty limited...

This all seems perfectly normal. You simply said "Thanks for the feedback!" and then moved on, right?

During that conversation, I even said something like, “I’ll let the boss know we did this together.” But when I later sent the final result to my boss, I didn’t mention him by name anymore, because in my mind his contribution felt minor and rushed compared to the whole project... Now I’ve found out that he complained... He seems really upset.

Contrary to other answers and comments discussing different workplace or cultural norms regarding credit and acknowledgements, I'm going to focus on a different point: you broke your word.

It seems quite possible to me that this is the major root of your colleague's displeasure. In many workplaces it is common for colleagues to help one another out - even in an unacknowledged capacity - with a reciprocity of small favors. This quick 20-minute feedback chit-chat seems to fit that description. That being said, if after this kind of favor my colleague exclaims "You're a lifesaver! I owe you a billion!" I would take that thanks as simple overemphatic puffery; whereas if my colleague says "Thanks! I'm buying you lunch today!" I'd expect to actually be given lunch (and letdown otherwise). Presumably they are taking your commitment of "I’ll let the boss know we did this together." just as literally.

Now I’ve found out that he complained to my boss and even gossiped about me, saying I didn’t acknowledge his input. He seems really upset.

Were I promised a lunch never delivered, I'd have probably just made a mental note to heed my coworker's promises less moving forward, and maybe complain to a another coworker if it seems like a recurring issue. Escalating complaints directly to a boss seems odd, perhaps there is more to the story?

If you share a boss, I could imagine a scenario where "Hey boss! How was ABC's report on XYZ? Did they implement my advice on improving LMNO and PQRS?" is met with a very awkward "Did you really contribute on this? ABC made no mention of you." or similar response. Now they are in the poor position of looking like they were trying to steal (or at the very least overstate) undue credit on your project. Perhaps their strange escalation and gossiping is some sort of clumsy "damage control" response to a situation like that?

Did I mess up badly here? How should I handle this with my colleague and with my boss going forward?

You messed up in a couple ways, but nothing particularly bad that cannot be bounced-back from.

The first mistake was a small error in committing to "overpay" for a small favor. This was not a problem for anyone except you - and even then the excess "cost" was nothing more than the minor inconvenience it would take you to spend a few moments writing "Thanks to DEF for their feedback on LMNOP." on an email or presentation slide. It should have been a small price to pay for a simple calibration re-tuning while getting to know the culture of reciprocity at your new workplace.

The second, and much bigger mistake, was consciously choosing not to follow through with even such a small commitment. At a minimum it hurts your reputation to the person you directly broke your word to (making them less likely to provide feedback, etc. in the future)... but as you're learning now that kind of reputational damage can spread wider than just the person you let down.

As far as fixing things moving forward, my advice is similar to the other answers: apologize for the issues you've caused, and learn from it moving forward.

(Granted, you'll probably have to fib a little and say "Sorry for forgetting to acknowledge you and breaking my word." rather than "Sorry, I thought I'd get away with it.")

For both colleague and boss: Admit the mistake, say oops, say you'll try harder.

Then try harder.

Interpersonal conflicts and misunderstandings sometimes arise. It's important to accept that and resolve them, rather than getting defensive about them. "I see why you feel that way; can you accept that this wasn't my intent, and that I've learned from the experience?" goes a very long way.

Ask your boss what's normal in your organization.

I have always treated reviewing things as a part of the job. I don't expect any special recognition because I reviewed a document or a bit of software. There's always the possibility that your colleague is desperate for recognition and is trying to put the new guy down.

Don't make excuses for yourself.

"it was never my intention to take credit for his work", but it is exactly what you did. Own your mistakes, because that's the only way to get better.

As a good gesture, probably treat him for lunch and apologize. You don't have to INTEND to make mistakes, but you DO need to be intentional in correcting them.

this is such an easy mistake to make when you’re new. You didn’t try to take credit; you misread how much the shout-out mattered to him. I’d keep it simple and kind: have a quick chat, own it, and fix it. Something like, “I’m sorry I didn’t mention you after saying I would. Your feedback did help. I’ve learned from this and I’ll make sure you’re credited properly.” Then send your boss a short follow-up note acknowledging the colleague’s input so the record matches your intent. Most people just want to feel seen; a sincere apology plus a visible correction usually resets the relationship.