The West Country club got their season off to a disappointing start as they went down 22-16 at Kingsholm Stadium.
"We've shown very, very short glimpses about what we are about, but it's embarrassing," Simpson-Daniel told BBC Sport. "We've got to face up to the fact that it wasn't good enough.
"It was horrible for everyone involved. It leaves a bad taste in the mouth until the next week when you can try to put it right."
Gloucester have the chance to record their first win of the campaign on Sunday when they travel to Saracens.