Yates admitted his side took a "battering" at Sixfields but Aidy Boothroyd's Cobblers only have one goal to show for their efforts heading into Sunday's second leg at Whaddon Road, where the Robins are unbeaten in 20 npower League Two matches stretching back to mid-September.
Roy O'Donovan's acrobatic finish, his sixth goal of the season, settled matters midway through the first half from Chris Hackett's right-wing cross. And Yates said: "We're 1-0 down at half-time, we knew we'd have to win our home game."
He added: "We've got a great home record, one of the best in the league, I'm probably a happier man than Aidy right now. We got a bit of a battering, we didn't play anywhere near our best but to be fair to my back four and particularly my two centre-halves, although we've had to deal with a lot of crosses Scott (Brown) has had one save to make.
"I'm disappointed with the goal, how it came about. Credit to them, they were miles better than us and we've got a chance. Game on on Sunday."
It was Northampton's first win in seven attempts over the Robins, who completed a league double this season, but they will be fully aware that they have failed to match their impressive home record on their travels this term.
Boothroyd admitted the tie remains finely poised but is confident his side more than have the ability to see the job through.
"We've given ourselves a good chance against a good team in the second leg," Boothroyd said. "We've worked so hard and played so well that you want to finish it off, but Cheltenham will still fancy their chances.
"The second leg of a play-off you know what you've got to do, you know what it's all about and we think we can go and score at any place, we've proved we can do that. We've got to make sure we keep very, very solid because we'll get an onslaught and we'll have to be able to deal with it.
"It means Cheltenham will have to approach the game differently and so do we. The tie's wide open, it's only half-time and we've got to make sure we go there and get a very good result."