The Dons dominated possession against the newly-promoted Staggies in Saturday's SPL clash at Pittodrie, but lacked the cutting edge to break down a stubborn defence in front of a healthy crowd of 14,010.
It was the first-ever meeting between the sides and Adams was content to come away with a point.
He said: "I'm delighted as it's not easy for a football club like Ross County to come to Aberdeen where they are allowed to spend the money they do on the likes of Niall McGinn, Gary Naysmith and Jonny Hayes. They are players who have undoubted ability.
"We are not in that league in terms of signing players but we are a team that is well organised with a desire to do well this season."
Ross County are now sitting eighth in the Scottish Premier League table following two successive goalless draws.
However, Adams admitted his side will face a tough task to extend their unbeaten run when they face champions Celtic next week.
He added: "That's a year that we have gone unbeaten in the league. It's great because we had two difficult games against Motherwell and Aberdeen to start the campaign off.
"We only have the small matter of Celtic next week! They are away to sunnier climes this week, while we will be stuck in Dingwall."
The Dons were dealt a setback when former Celtic winger McGinn, playing in his first home match for the Dons, was stretchered off after landing awkwardly following a collision with County defender Grant Munro.
Manager Craig Brown said the player will now miss out on representing Northern Ireland against Finland this week.
He said: "Niall was included in the squad for midweek but he won't have any chance of going there because he has twisted his ankle. I thought it was a head knock at first because he was holding his head but I think that was just out of his disappointment, not only from the point of view his club Aberdeen but also the Northern Irish team.
"We can't tell the length of the recovery period but he will certainly be out in the immediate future."
The Dons manager was frustrated that his side did not manage to score the elusive goal that would have given them a first win of the season.
He added: "I'm disappointed we didn't win, given the amount of possession we had. The lads are in there apologising for the misses, Gavin Rae is distraught and Scott Vernon is the same.
"If you are a fair-minded, independent person you would think that we were well on top in terms of play and chances but we paid the penalty for failing to score. If they play as well in the rest of the season and make the same number of chances then I'm quite sure the results will be different."
