Explain this baseball ruling to me from ATL game yesterday

I follow/played a lot of baseball, and I cannot figure out the reasoning for this. In yesterday's ATL game, Mike Minor was charged for an unearned run. This was the scenario:

Top 8th, Minor gets first out and then gives up a double. Venters replaces Minor pitching and gives up a single. This puts runners on first and third. The next batter hits a come backer to the pitcher, and Venters throws home and gets the runner out (the inherited runner/Mike Minor's runner). This mean that Minor is no longer responsible for anyone on base. Later on, Uggla makes an error and allows the hitter that Venters gave up a single to to score (unearned run because with two outs). How is that run charged to Minor when he never even faced that batter?

Here is the MLB play by play
Defensive Substitution:

1.Corey Hart grounds out, shortstop Jack Wilson to first baseman Freddie Freeman.

2.Jonathan Lucroy doubles (1) on a line drive to center fielder Michael Bourn.

Pitcher Change: Jonny Venters replaces Mike Minor, batting 9th.

Coaching visit to mound.

3.Mat Gamel singles on a soft line drive to right fielder Jason Heyward. Jonathan Lucroy to 3rd.

4.Cesar Izturis reaches on a fielder's choice out, pitcher Jonny Venters to catcher Brian McCann. Jonathan Lucroy out at home. Mat Gamel to 2nd.

Offensive Substitution: Pinch hitter Norichika Aoki replaces Shaun Marcum.

5.Norichika Aoki singles on a ground ball to second baseman Dan Uggla. Mat Gamel scores. Cesar Izturis to 3rd. Throwing error by second baseman Dan Uggla.

6.Rickie Weeks strikes out swinging.