The First Division champions extended their unbeaten league run to 38 games after conceding just one goal in their opening four SPL matches.
That goal, a Kris Commons equaliser for Celtic in the third minute of injury-time, prevents the Dingwall side being top of the table.
County also held Motherwell and Aberdeen to goalless draws and won 1-0 at Dundee.
"I'm delighted. The players have progressed and adapted to the Premier League," Adams said.
"They have shown a good organisation and togetherness that's been able to keep this unbeaten run in August and we hope to continue that in September.
"Obviously it's a new league for us and we knew it was going to be difficult.
"It was a difficult start and we were unfortunate not to pick up more points, with the last-minute goal against Celtic."
Adams has been busy with managerial duties today, allowing Steven Craig to move to Partick Thistle on loan until January 28, which could allow him to add a player to his squad.
"He hasn't been able to push himself into the team so it's probably beneficial for both of us to get some game time at Partick," Adams said.
"We can take in a player and we're still looking at that."
That player could yet be former Hibernian striker Derek Riordan, who has been training with County.
"There's still a possibility," Adams said.
"We are talking to his agent.
"His agent is away with Motherwell just now in Europe. But the stumbling block is obviously going to be wages."
There was some bad news for Adams ahead of the SPL visit of Kilmarnock.
"Mark Corcoran is out for Saturday, he's got a groin strain. We'll miss him because he did exceptionally well against Celtic and Dundee," Adams added
