No. You cannot. There is strict control over liquids and you can only pass security with 100ml bottles. Since carry-on must pass through security, you cannot have a 750ml bottle with you.
When you buy Duty-Free at the airport or even non duty-free, you buy them past security and they are items the airport considers secure.
There is a subtlety which may even make the airport refuse to sell it to you. When you buy from duty-free you show your passport and boarding pass, if they know that based on your itinerary you will have to make it through security again, many shops will refuse to sell you large bottles. This happened to me several times. Last time when travelling from Taipei to Quito via San Francisco, the duty-free in Taipei did not let me buy liquids since I would have to clear security in San Francisco. Now, I have also seen some airports allow sealed duty-free items bypass security when changing terminals that also require a security check. This varies by airport and terminal.