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The vinegar (acid) dissolved the cement at the surface of the concrete leaving the aggregate (sand + gravel).
You can buy small bags of portland cement here at Lowes and probably Home Depot. You don't want to use any pre-made concrete mix with gravel and/or sand because all you need to replace is the cement. Take this cement powder, add a little water to make a paste, dampen the area that needs to be repaired, apply the cement paste to the damaged areas, press into the damaged areas and trowel smooth with a steel trowel.
The new cement vs. old concrete will be visibly different in appearance, but you should be able to get it smooth and sealed with this approach.
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