Your players will lose a bit of stamina after every game (except if you're playing myClub friendly matches). You don’t need to refill it all the time, but that’s something you should keep in mind after 3 games or more.
You can rest your players, so that stamina gradually recovers in the background. You can also switch to your SIM team for 1 game so that your whole team rests up.
You can also use a Stamina Recovery Item to get a player back to 100%. To use them, you will need to go to the CLUB HOUSE / SQUAD MANAGEMENT screen, pick the player you want and then press the "Player Menu" button. You will see a "Stamina Recovery (single)" item.
You can also replenish your whole team's stamina, although that's rarely a good use of Items. To do so, instead of picking a player, press the "Team Menu" button and use the "Stamina Recovery (All)" option.
These items are awarded to you as daily login rewards or after completing a certain number of games/actions.