4-1-4-1 is hard to break down as is the 4-4-2 classic at times because it is basically a more defensive 4-5-1.

you had more possession in both games but that counts for squat these days with this engine.
Attacking mentality is not the cause as posted by the previous poster. 4-5-1 will come out ahead of 4-4-2 most of the time because of the midfield extra man and the fact that the formation is both defensive and offensive depending on the mentality and orders/tactics.

You could have switched your formation to either 3-5-2 or 3-6-1 in order to take advantage of a defensive formation and really put it to him offensively, since the best defense is a good offense for the most part.

Anytime someone plays with only 1 ST, you should automatically think of only using a formation with 3 DC, because to do otherwise is usually a waste of a defender where you can put in an additional MC or ST and make a difference in the game. So lets start there.

3-6-1 butterfly down the flanks, attacking, hard tackle should have beaten his 4-1-4-1. 3-5-2 flat or even 3-5-2V should have gotten a better result as well. once you set your defense, then try to make sure you equal or better his amount of midfielders, so you dont get overpowered in midfield and lose the possession battle.

Just try to be more flexible in formation if you want to succeed at this game. The game engine is fickle and 4-4-2 is not good enough to beat everyone all the time.