Please remember, no one is saying you can't give young players a chance. As someone else has already pointed out, you can use the 3 subs available to you if you want to give someone a run out and you are comfortable with it. You just have to be more cautious in when and how you do it in case you get an injury after you've used your 3rd sub like Chelsea did in last years FA Cup against Newcastle.
Also you can start these players. Although most teams will start with their strongest 11 in competitve matches, they can start some of the more inexperienced players in games that are seen to be less competitive.
Also I have found that if you have this limitation, the fringe players try harder in practice to impress to get a starting position, and always try harder when they do get the chance to show what they can do. Those chances will come every season. Players will get injured, suspended, lose form, or be on vacation. There will be plenty of time and opportunity for non-starters to get a chance.
Usually if they are up to it they grab that chance with both hands and then you have something that any coach loves to have: Competition for starting places.!!!!
