Moen faucet, how do I tighten this?
Tightening a Moen Faucet Lock Nut - Home Improvement Stack Exchange
Moen Kitchen Faucet has loose cover, how to fix? Handle is still working, it’s just the handle cover that is loose and won’t push back in.
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You could try one of these tools to see if it would get up in there to tighten the faucet anchor nut.
It would be used something like this:
I also wonder about whether you should have first removed the rusty old washer (A) and the dried plumbers putty (B) before installing the new faucet.
First off it seems very likely that the replacement faucet would have come with a new washer. And secondly it would be much easier and secure to tighten the nut against a new washer surface.
Usually you put a bead of plumber's putty around the faucet base to seal where it meets the sink. When tightened the excess should squeeze out, which can be wiped away.
It looks like there are #8/32 or #10/32 tapped holes in the nut. I agree with Michael, put a new washer under the nut, then try a basin wrench or put a screw in these holes to gain more leverage. Alternatively, put screws in all three holes, and use those to tighten the whole thing with a screwdriver, instead of a wrench. A new washer is definitely a good idea if going this route.