Tom Pope, voted the best player in League Two by rival managers last weekend, ended an 11-game barren spell with a matchwinning hat-trick to take his season's tally to 30 goals, ensuring efforts from Kaid Mohamed and Paul Benson proved mere consolation.
It leaves the Robins still in fifth place in League Two, just one point adrift of the top three, but now having played two more games than their nearest rivals.
Yates said: "We will have to win our last five games to do that (secure automatic promotion). It's possible and we are capable of going on a run, but I'm not stupid and we were looking for three points here.
"In fairness to Vale we fell apart for 20 minutes after the first goal and the game could have been over by half-time.
"But there were a few home truths said back in the dressing room and we got the right response in the second half.
"When Paul Benson put us in front they had gone, but fair play to Pope because he lifted them again and he's been on fire this season.
"He's scored three good goals from his perspective, but they were poor from our viewpoint. The first two have come from corners and should have been dealt with and we've got caught with the third after a clearance from our 'keeper.
"It's disappointing to say the least, but we've got to put this behind us and remain positive. There is still everything to play for."