It's irritating to kill the enemy's hero or destroy their main building (basically completing the mission's objective) & then having the game show the "Click to finish game" parchment without giving time for the player to collect the loot.
Once a mouse click is registered, the mission ends.
Heck, that was even once when I was in the inventory transferring loot & the Finish game prompt came up. I was transferring an item midway & lost the item when I clicked the mouse.
Is there a way to loot items in chests after completing a mission?

Short answer - not to my knowledge.
It's always been a frustration for me with each of the games. The only thing that redeems it is that usually when you're about to win you have plenty of time before delivering that killing blow. Unfortunately that's not the case with assassination missions.

Once the victory image appears, no, I don't believe there is any way to continue looting. It's mostly a matter of keeping your hero close enough to the action that you can nab items before winning the scenario. It often devolves into a mad scramble for me as I grab what I can as quickly as possible.
You can still open the inventory and move your hero around while the victory cheering is playing, though. You have to use the backpack icon next to the hero portrait, because the "i" hotkey stops working for some reason. It's only 10 or so extra seconds, but sometimes that's just enough.

Thanks for all the replies.

In the end, I remapped the Pause key to the spacebar.
If the victory image appears, I could still manage my inventory while the game is paused.
This isn't a solution to continue looting after the Victory image appears though.

The developers should have just let the players end the game manually after victory is achieved.