Most resources in the game have a limit on how many you can have in the inventory. You can play battles normally, and you will start earning the resources again once you’ve spent some of them to make space in the inventory.

These are the maximum amounts for different resources:

Rune Keys - 1000
Runes - 50
Friendship - 750
Energy Berries - 25
Arena Tickets - 25
Hatch Tickets - 25 (Bronze and Silver)
Premium 10x Hatch tickets – 10 (gold)
Dungeon Keys - 75
Totems - 120 (Prestige and Super Shot)
Anger Totems - 100
Evolution Material - 18000 (of each color)
Evolution Essence - 400 (of each color)