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The Robins trailed at the break, with Nahki Wells putting Bradford ahead early on, but a brace from Jimmy Spencer followed by a third from Ben Burgess sealed Cheltenham's third straight home win and guaranteed them sixth place.
"The lads have not been on the end of any harsh words for a while, but it was needed because in the first half we didn't do anything properly," Yates said.
"We improved a lot after the break and that's credit to the players. The first part of what we set out to do has been achieved. We can now have a quiet week, go to Plymouth and give one or two lads a rest and then start preparing for the play-offs.
"The first half was poor and we made poor decisions and defended badly. We didn't keep the ball, we didn't pass the ball and we could only get better.
"Kaid Mohamed came on and made a big difference. I told him he'd play a big part in getting us where we need to get to and I thought he was outstanding in the second half. We lacked a bit of pace and when we opened the game out a bit it suited us and the lads responded superbly."
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