How do you deal with messing up at work?

I’m in customer service and I process orders.

I work with someone who sends me orders and they’re very particular. They want the order confirmed that I processed it and confirmed that the vendor received it. My company is extremely large and scattered throughout the US.

He sent me 3 orders on Tuesday and today asked if the vendor received order xyz. All 3 show checked done in outlook but order xyz wasn’t processed.

I immediately processed it and the earliest it can ship out is Thursday. I’d have to contact the vendor for it to be pushed out any sooner. The vendor is super vocal to people I work with about basically anything so asking them to get the order out sooner isn’t a good idea.

I don’t know what to do. I could just leave it be and see if anyone says anything? It’s possible my co-worker will ask for an ETA sometime next week and he may ask why it’s so delayed when it was due today. Or he might not ask anything.