Does Instagram Insights show how many DMs a post brought in?

No. Insights counts reach, likes, comments, shares, saves, profile visits and follows for each post, but not the conversations a post started. To know which posts bring in DMs, you have to link each conversation to its post yourself, automatically where Meta passes a source and by hand where it doesn't.

This gap is why so many agencies struggle to prove Instagram works. The metrics Instagram gives you are about attention. The thing a client pays for, people asking to buy, happens in the DMs, and Insights doesn't connect the two.

What fills the gap:

1. Link conversations as they arrive. Story replies, shared posts, ad clicks, ref links and comment private replies carry a source. Everything else gets confirmed by whoever handles the inbox, while the conversation is fresh.
2. Count per post, not per month. "Instagram brought in 23 DMs in October" is weaker than "the menu reel brought in 9 of them, and 4 booked".
3. Keep the method visible. Report how many links were automatic, how many were confirmed by your team, and how many are unknown. Clients trust a number more when they can see how it was counted.

Once you have a few months of this, you can answer the question that matters at renewal: which kinds of posts actually bring in customers for this client.

The full method is in How Agencies Prove Instagram Brings In Leads (When Google Analytics Can’t See Them).