If this happens again, you could do the following:
1. In the meeting with VP, admit that you missed the email, or too busy to correct. Thank him for pointing this out. Give him the credit in front if VP.
2. Talk to Magager A off-line, thank him again, but tell him it would be appreciated if he can take it to you directly in the future. Be poliet, professional but very firm with him. Be honest with him on how you feel. Ask him to put himself into your shoes.
3. Talk to VP in your next 1:1, bring it up casually by saying: " By the way, I sent out the corrected file after our meeting. I also implemented a process to capture the mistakes. Human errors do happen, it is important to have a process to capture those errors. I also talked to Manager A to thank him for the help and set the expectations on how to collaborate with his team going forward."
I guess you still can do number 2 and 3 now. Good luck!