Don't use a single sprite! For what you want to do a tilemap is the way to go. Because a tilemap re-uses identical tiles, it saves you a lot of memory and is also more efficient to draw on screen.
Use this tool to extract the tiles from your map image:
delete all doubles and create a tileset.
Then use this tool to create your map with the tileset you made before:
The maps you create with this tool can be loaded directly into Construct 2 (read the manual
on how to do)
I advice you to search the internet on general information about tilemaps in video game design
for you get an idea of how it works.