Solomona has been banned until May 8 for making a homophobic slur directed towards Worcester Warriors' Jamie Shillcock in a Premiership match last month.
The 24-year-old disputed the charge but was found guilty by the Rugby Football Union on the "balance of probabilities", as neither the footage nor the officials' microphones picked up what was said.
The Sharks have offered their backing to Solomona but have confirmed they do not intend to appeal.
Sale's statement read: "[Denny] is a decent and honest person and maintains that no homophobic words were exchanged. After serious consideration, Sale Sharks have come to the conclusion that there are significant risks as well as legal and financial hurdles in pursuing an appeal.
"As a consequence, Sale Sharks do not believe that it is in the interests of either Denny, the club or the game of rugby union to prolong this sad affair."
The statement added: "The Rugby Football Union disciplinary panel decided, on the balance of probability but with absolutely no other evidence, that Denny had said those words based on Jamie Shillcock's reaction only."