You didn't fall out of first because of interleague play. You were a game out of first after sweeping the Nationals, but then they continued winning while you started losing. you went 3-15 against interleague opponents, they played much better against the AL. By the way the Cardinals are in the NL and they were the first team you played coming back from interleague, you lost 2 out of 3 against them. During your 6-18 streak you 3-5 against the NL (including getting swept by the Braves in games 4 through 6 of that 24 game span). Besides its not like you had to play the Orioles,and the Yankees (1st and 2nd) like the Braves, Nationals, and Mets all had to (and look at that they're all ahead of you).
Interleague wasn't your issue, your team's performance was the issue, besides next year you could be singing a different tune about interleague play.