The Staggies have had a difficult start to the season and sit second bottom with three points from six.
They have now faced Hearts, Hibs, Celtic, Rangers and Aberdeen.
“I would hope a win isn’t far away,” he said. “We’ve had a real run against the top clubs, but we’re in games right to the end.
“I’m seeing signs. If we keep playing like that, we’ll be fine."
He added: “We’ve had Celtic, Rangers, Aberdeen, Hibs and Hearts now over the last few weeks and we’ve created good chances against them all, with good patterns of play.”
County were competitive against Hearts, posing a threat and could even have nicked a win at the end.
“We were playing against the team of the moment, who have a fabulous squad of players and are obviously flying in the league,” Mackay said.
“They came here today with an interesting change of formation from the one that has been serving them well.
“I felt we coped with that quite well.
“It was a very good game and we’ve, again, gone toe-to-toe with one of the best teams in the league.
“I was delighted with the way we scored both goals - they were excellent - and we could have nicked it at the end.”
Since replacing John Hughes, Mackay has undertaken an extensive rebuild.
A lot of Premiership experience departed, players like Michael Gardyne, Ross Draper and Iain Vigurs, while many of those who arrived are new to Scottish football.
“It is the start of something new,” Mackay said. “We’ve had 12 players in and 16 out, with everybody getting to know each other and debuts every week.
“It means it is going to be a rocky start, but what they’re giving me is organisation, commitment, determination, fitness and they’re keeping going to the end.
“Hearts were throwing everything at us yet they still go up the park and arguably should score in the last minute.
“I’m delighted with the way they’re applying themselves towards the way I want them to be.
“We’ll get there.”