The Irn-Bru First Division champions sensationally sealed their place in the Clydesdale Bank Premier League top six earlier this week in their first season in the top flight.
Adams admits his team have surpassed his own pre-season targets - but they will not settle for the fourth place they are in now. A top-three finish would guarantee European football and that is the aim as County prepare to face Hearts at Tynecastle on Saturday.
Adams said: "It'll be difficult, but we'll keep on going. We have done more than we could this season, the aim was to stay in the SPL, but with six games to go we cemented our position in the top six.
"So we really excelled this season, and that's great for the players of this football club.
"We are trying to pick up as many points as we can between now and the end of this season knowing that we've got that top-six status for our first SPL season, but Inverness and Motherwell are ahead and they both are playing very well."
Ross County have lost only twice since strengthening in January with the addition of the likes of Steffen Wohlfarth, Evangelos Ikonomou, and Ivan Sproule. Hearts have only won one game in 10 but Adams knows the game will not be easy.
"Especially at Tynecastle, it's a difficult venue to go to," he said. "They play so well at home, they get balls into your penalty area quite quickly. Earlier on in the season they had a lot of long throws, and all the final third entries - we have to guard against that."
Adams confirmed Paul Gallacher would be in the squad after signing on a short-term deal after being made redundant by Dunfermline. Gallacher was brought in to challenge for the number one jersey after Mark Brown was ruled out for the season with a broken hand.
Adams said: "He's come in and giving Michael Fraser some back-up, he is pushing him along as well, and it's always good to have competition. It's amazing when you take a new player, in certain areas, it boosts the player that is already in that position, and makes him play even better."
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