This was the same issue with me, one of those things that frustrates you, but i always know the game is meant to be hard, it's meant to feel like Football Management. So, i thought about it.
I tried changing to counter and even changing my formation. That didn't really work. Now, everyone says, to play fast on the counter attack, you need to make sure your tempo is fast with a direct playing style. Now that generally will work, but sometimes, you have to know the opposition and the way they play.
When you are given a team report by your assistant, check which formations they conceed the most against and play with that one if you have players in the correct positions.
For away games, i tend to play with the Counter Attacking style, balanced (not rigid or fluid). Direct passing, Man Marking and Drilled crosses, leave the rest default. With the sliders, i tend to make the tempo quick and width medium. Leave the other slider unticked.. Finally, tick the counter attacking box and if you have fast defenders, the play offside setting.
The formation i tend to use is a 4-2-3-1. 4 at the back, 2 defensive midfielders, 2 attacking wingers, one centre midfielder and a striker. The reason i do this is because when counter attacking, it can be very fluid when one of four defenders gets the ball to a DM, from there onto the CM, and he can spread it wide, and then the attack can really get going.
You can either go with that formation, or if you think its a little too defensive, even just play with one defensive midfielder, one centre midfielder and an attacking centre midfielder, with the striker and two wingers again. That works aswell. Even playing like this works at Home, you draw the opposition in, and swoop them on the counter.
Hope this helps, i had my struggles, but that's how away games are in the real world, not as easy as home games as the opposition always puts a bigger effort in.