Naughton was optioned to Triple-A Salt Lake on Wednesday.
Naughton was charged with the loss Tuesday when he allowed four runs in two innings against the Rangers, and it's not yet clear whether he'll pitch during the Angels' final series of the year. The southpaw has made seven major-league appearances (five starts) in 2021 and has recorded an 0-4 record with a 6.35 ERA and 1.81 WHIP in 22.2 innings.