Been there. The problem is that a 9x12 rug is meant to fill a 9x12 room and comes out to be 8 something by 11 something.
I've yet to find anything that is actually 9x12 so if you love it, keep it. Finding a 10x14 is no piece of cake, either. The other suggestion would to get a rug bound to the size you need. Otherwise, learn to ignore like I have all these years (an end table would cover the difference and no one would even notice).

I agree with jaysmom.

My 84" sofa sits on the 96" end of our 8'x11' rug. It's the same situation as you and I think it looks fine. I have chairs facing the sofa with a table in between and I matched the 6" of rug showing.

I have a sofa table and no side tables. I think trying to put end tables on either side would look funny because they would be half on the rug and half off.

Here's my living room. Ignore all the dog stuff and furniture covers for the dog. We have a puppy and he has completely overtaken our lives at this point. :-)

IMO whether this rug is the correct size depends on what else is going on in the room. Need more info and pics would help.

IMO many people often choose rugs that are too small but there is a place for small rugs in certain spaces.