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 today. 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."
County boss Derek Adams was left to rue a host of missed chances.
He said: "We had a lot of chances but we didn't take the opportunities when they came along. I think we could have been here until tomorrow and we still probably wouldn't have scored.
"We've had a lot of opportunities, but they defended in numbers. They had that many players in the area. I didn't think they troubled us until late in the game. Michael Fraser has not had a save to make and I thought Cammy Bell was outstanding. You can see why so many clubs are after him.
"But we've had a terrific season. There are two games in midweek and if they go for us it will help relieve the pressure before the Hearts game next Saturday."