Aru attacked just beyond midway up the 8.7km climb of Mont du Chat, just as Froome raised his hand to indicate to the team car that he had suffered a rear puncture.
The Italian said that he didn't see Froome's puncture or his hand go up before going on the attack, an assertion that Yates described as "absolute bulls***."
Froome was able to get a spare bike and ride back up to Aru, who had been followed by the other main contenders, but that didn't seem to changes Yates's interpretation of the attack.
"I think it was a dirty move," the Orica-Scott rider said after the finish. "I don’t like what he did but this is a bike race and he can do what he wants."
"I can’t find the words to say. It’s not something that you do. We should have respect for each other. Chris had a problem there, he wasn’t getting dropped and there was still a long way to go in the stage.
"I’m not going to have any grudges but maybe some of the other guys will do. From what I saw it wasn’t the correct thing to do."
Yates finished in 11th place on the stage, in the same group as Nairo Quintana (Movistar) and Dan Martin (Quick-Step Floors), 1-15 behind the front group having managed to avoid crashing on the descent which saw Richie Porte hit the deck and abandon the race with a broken pelvis and collarbone.
"I think the organisers wanted to spice things up," Yates said referring to stage nine's unconventional route, featuring narrow climbs and descents which rarely feature in the Tour.
"They’ve seen Sky set the tempo the last few years and they want to spice things up, with small technical roads. I don’t think that there’s anything wrong with that and it makes for exciting racing."
Watch: Tour de France stage nine highlights
Yates now holds the white jersey for best young rider by nearly three minutes over Louis Meintjes (UAE Team Emirates), despite suffering on the final climb and being dropped by the yellow jersey.
"It was another level today. I’m pretty tired and I gave it everything. I almost got dropped from my group but I’m happy with my ride. I gave everything that I had.
"I’m looking forward to the rest day because I’m absolutely f*****. Sorry. I don’t know another word to describe it."
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