An early goal from James Fowler gave Killie a lead and they managed to hold on to despite constant pressing from the home side.
Shiels said: "People think Ross County had a lot of possession, but we got our goal and the tactics were to go deep and forfeit possession in their half of the pitch so it looked as if they were dominant.
"We knew we would have to defend a lot of corners so it was a great learning curve for the kids but we coped okay.
"We used different methodology to win the game. We played Ross County at their own game and Cammy Bell had one save to make."
With a game in hand, Killie have a top-six finish in the Clydesdale Bank Premier League in their sights.
Shiels added: "There's a long we to go. We finish with two homes games, but they are very difficult ones.
"There are no easy games in this league. Forty seven points is our target, but we've got to win our next game, that's our game in hand. If we can get something from that it puts us in a decent position."