A 1-0 win at fourth-placed Hibernian, courtesy of Brittain's second-half header, took 11th-placed County nine points clear of Dundee, who lost to Celtic.
"We're not worried about what's below us," Brittain said.
"We're trying to focus on what's above us and to try to strive to get ourselves up the league.
"I'm a great believer that if you keep looking behind you, that's the way you'll go.
"If you keep looking onwards and upwards, that's the way you'll go and that's the way we'll continue to work."
The win at Easter Road was County's second over Hibs from two attempts this season.
Hibs are seven points better off than County and targeting a place in the top six this term, but Brittain played down his side's chances of taking a place in the top half of the table in their first season since being promoted as Irn-Bru First Division champions ahead of Dundee.
"Yes, we want to finish as high up the league as possible, but at the same time we've got to set a realistic target," Brittain added.
"If you look over the course of the season so far, I think it's a fair return of points we've got."
County play Hearts in Dingwall on Saturday, seeking a second SPL victory over Edinburgh opposition in four days.
They will have to do so without Stuart Kettlewell, who is out until after the winter break after pulling a hamstring in the second half at Easter Road.
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