Manager Mark Kerr praised his Ayr team for controlling Premiership side Ross County to win 1-0 at Somerset Park.
Stephen Bell's 36th minute goal was enough for Ayr to cause one of the shocks of the Scottish Cup fourth round.
Kerr felt his team were never in danger of conceding their lead despite Ross County creating the majority of the chances.
"We felt we controlled the game and gave out the balls in the right area and capitalised when we found space," Kerr said.
"We knew they would try and get in behind us and stretch us.
"They are a Premiership team and you know it is going to come off three or four times for them but you try to stop it.
"But we also played a nice combination of passes and got onto the second ball. We were picking up balls in the middle park that we usually don't do.
"It breeds to confidence to see we can play both ways."
Ross County had a golden chance to take the lead after 20 minutes when Harry Paton sent a perfectly weighted ball for Lee Erwin. But his low drive was well blocked by goalkeeper Ross Doohan.
Ayr were rewarded when they broke the deadlock nine minutes before half time when Bell beat County's defence in the air to nod Stephen Kelly's corner kick into the net from six yards.
Ross County could have equalised in the second half when Billy Mckay beat the Ayr defence to Josh Mullin's cross from 10 yards out but nodded wide .
Ross County co-manager Stuart Kettlewell had no complaints about the result.
"We got what we deserved out of the game," he said.
"We will not say because we had so much of the ball in the second half we deserved a draw.
"It is miles off what we expect in the two years that I have been in this job."
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