Kirk Cousins is opening up about the blockbuster trade ... telling TMZ Sports why he's bummed to leave Washington but stoked about getting courted by guys like Von Miller.

With the Redskins trading for Alex Smith, Cousins is moving on -- he's the hottest player in free agency by far.

Cousins says he understands why Washington did what they did -- "Team's gotta do what's best for them" -- but says he'll really miss the people in Washington he's known since 2012 ... from teammates to the team chaplain to neighbors in the community.

Watch the clip -- you can tell Cousins is emotional about it.

The good news ... Von Miller has been saying he REALLY hopes the Broncos make a move for Cousins ... and Kirk's flattered.

"It's flattering to hear a player of Von's caliber speak nicely of me."