Managing my players' fitness better

So within the last couple of seasons, my teams in 011 English and 014 English have both reached the Champions League. Having had no prior European experience in Simsoc, it was quite a shock to the system when my fixture lists suddenly became congested as heck and my players' fitness levels plummeted. I know that the best way to combat an unfit squad is simply to get a larger squad, so you can rotate more, but I don't have enough money to buy one high-level player, let alone ten. Is there any way I can improve my squad's fitness so they don't get so tired from playing so many consecutive games? Because my league form is taking a real hit >.<

In squad training you can set your players to Exercise Gym and this has the greatest effect on improving fitness but unfortunately will have a knock on effect on field skills although I am unsure how important these are.

Sadly, extra games means lower fitness so I tend to put weaker sides out in the cups until I reach the latter stages. European Cups are more important though so it's tough to keep your side fit. Just have to weigh up 2/3 matches ahead and decide which games you need your best players for.