Or the old classic hip pouch that goes through the belt. It depends what else you're wearing when cycling round in a tshirt, if it's casual then a hip pouch or bum bag. If it's lycra then get a bar bag.
I just bought a fanny pack exactly so I have somewhere for jersey pocket stuff without wearing a jersey. Love it wearing casual shorts and T-shirt on the fast road bike.
Or the old classic hip pouch that goes through the belt. It depends what else you're wearing when cycling round in a tshirt, if it's casual then a hip pouch or bum bag. If it's lycra then get a bar bag.