His side have won only two of their first seven league games following promotion and lie in seventh place.
"What I said at the start of the season, and I was very, very clear, was that we'd be highly competitive," the English manager told the media.
"You guys said about challenging Celtic and challenging Aberdeen."
Rangers are seven points behind reigning champions Celtic and three adrift of the Dons, who were last year's runners-up, after losing to both in recent weeks.
"I said we'd be highly competitive and that won't change," he said of a side beaten 2-1 at Pittodrie in their last outing.
"I think you saw on Sunday we were highly competitive, but we have to get the rewards for it.
"What we have to do is to turn our domination and ball possession into rewards.
"That's what we did against Queen of the South. Between the Ross County and Queens match, there was no difference between the displays, but in one game we were far more clinical than the other."
Warburton, who has received a one-match touchline ban for comments made after the loss to Aberdeen, insists it is still early in the season to express disappointment at Rangers' league position.
"You can say you are four points from the bottom or three points from second," he said ahead of Saturday's Glasgow derby against Partick Thistle.
"At this stage of the season, in any league, you win two games and the whole picture changes. The same if you lose two."
Mark Warburton says his goal at the start of the season was simply to be "highly competitive" in the Scottish Premiership and Rangers have done that.