Yates saw his side beaten 4-2 on Tuesday night at Crawley, who move above the Robins on goal difference at the top of League Two, as Tyrone Barnett and Sanchez Watt grabbed two goals apiece.
Everton loanee Luke Garbutt and Darryl Duffy notched for Cheltenham as both managers were sent to the stands.
"He got under my skin. I fell for the old one-two. The man is incessant. A lot of people don't like him and he questioned my integrity in the first half. He knows what he said," said Yates.
"He accused me of something and he's got under my skin. I fell for it. In the second half, with us 4-1 down, he said something. He wound me up. I didn't swear, but I defended what I'm about."
Yates had no qualms with the result and refused to blame the "ice rink surface" at the Broadfield Stadium, before calling on his side to forget about the game.
"I've no complaints. The circumstances didn't go for us," he added. "The pitch was bone-hard but we knew the game would be a tough one and it's best for us now to move on. After going behind unfortunately we didn't handle it properly and the damage was done. We then had to salvage a bit of pride. We won't play on a pitch like that every week."
