Think about what makes something look grimy. Here's a few ideas.
- Carpets get dust caught around the edges. Make your tile edges fade a bit near the walls. Make the fade irregular.
- Stains. Make irregular patches of a darker shade. This goes for the carpets and the walls.
- Detritus. Add some dark specks of... stuff. Better not think too deeply about what it is. Or if you want to think that deeply, draw them and add them in. Dead rats, syringes, cockroaches, whatever fits your genre.
- Distressing. Make some cuts, dents, or similar damage to your walls. Make threadbare, torn or worn bits of carpet.
If you want to do a concrete floor, think about things like multi-storey or underground car parks. What makes the concrete floor look grimy? Maybe:
- Stains.
- Cracks.
- An uneven surface with dirt ground into dips and pockmarks.
Find stock images for the things you want to draw and study them to see what makes them work. If you have a go at making some grime, we can probably give better feedback. What you have here is a blank canvas.