Mongols v. Mayans Post Imp Help

I recently played a very tough game as Mongols against Mayans on golden swamp. I got drushed and was playing from behind for a very large portion of the game. My opponent originally teched into plume which I countered with a defensive castle, knights and skirms. After holding and stabilizing I was able to push into his economy and raid a bit as I was going Imp (he was already imp and this greatly delayed his push) I then was able to fully tech into mangudai and was switching my focus to the middle to take the gold. I was able to take the middle and hold it for only a bit because by that time my opponent tech switched into eagles. Now I wasn't able to handle them and eventually lost the game. I am not exactly sure how I could have played better (I will watch the replay later) however, my biggest issue is in this kind of matchup is it an auto loss? Can Mongols not deal with post imp eagles? What counters post imp eagles in general from any civ?

Update: I went and sped through my replay and found a couple of tactical errors that if I had not made I could have probably won.

1. I did have a military advantage just after taking the middle then lost if after getting stuck in a corner.
2. I myself got raided and A should have put up some stone walls to protect my base and B after the raid ended immediately rebuild lost TC and farms etc.
3. Continue pushing into his base where I already created weakness and had forward castles, workshops etc instead of going to the side where I didnt have any of that.

TYVM age community.