Yep, the trick with the Mongols is never to go 1v1 against them but choose battles to fight to your advantage.

River-crossings are the major points you should look for (and bring as many Xbows and artillery as possible...). Use the bridge to bottle-neck them and fire away...

Defending sieges against them can also be a good way to fend them off. The Mongol cavalry loses one of its most fearsome capability in city streets or below walls : maneuverability...

For more advice, use the search engine and you'll find a few thread related to ways of defeating the Mongols...

They're tough for sure but not unbeatable... (as they were meant to be...). And I think you still manage quite well against them... You're scoring victories nevermind the odds !!