Oxi Clean has been my best friend for many other things such as laundry and cleaning my bathrooms.
I love that product and it removes a lot of tough stains.
Spray any of the stains down with the Oxi Clean.

Image by DIY Lily Ardor via YouTube
Then, take the hard bristle brush and scrub it down.
Repeat the steps again if the stains do not come off the first time.
Also, you might let the Oxi Clean soak in for about 5 minutes before scrubbing.

The vacuum sucks out the water and any excess dirt from the sofa.
I would try using a regular vacuum or invest in a similar vacuum like the one in this video.
Continue to watchDIY Lily Ardor tutorialon YouTube for full instructions and details.

Overall, this is an easy method to remove those stains off the couch with inexpensive cleaning supplies.
I know accidents can happen on the couch whether its spilling food or an accident from a pet.