New draft pick dropped me out of a match

Did you lock in your champ? If you don't actually hit the button it counts as a dodge.

You need to lock in before the timer runs out; otherwise, the new champion select will pop you out of the lobby.

No More Surprises Now each player selects their champion one at a time. For example, if your team has first pick, the opposing team still picks two champions afterward, they just lock in one after the other. As a result, however, both bans and picks now require everyone to lock in their choice. If a player fails to lock in a pick or ban, champ select ends and players return to queue (and that player faces the same queue dodge penalties).

http://na.leagueoflegends.com/en/site/2016-season-update/new-champ-select.html

It did it as soon as I clicked my champ