Their first league contest in four years proved a one-sided affair as Moussa Dembele's treble helped Celtic open a four-point gap on their rivals.
"It's game five of a long season," Warburton said. "We don't see a major gulf. We just got beat 5-1.
"They have bragging rights and deserved to win."
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The former Brentford manager saw new signing Joe Garner give his side a lifeline with a goal just before half-time to reduce the deficit to 2-1.
However, he accepted the blame for their crushing defeat after going for broke once Scott Sinclair had made it 3-1 to Celtic just after the hour.
Warburton replaced one forward, Kenny Miller, with another in Martyn Waghorn. But when centre-back Rob Kiernan limped off injured after 72 minutes, he sent on winger Harry Forrester, rather than another central defender in Clint Hill.
The move backfired when Philippe Senderos picked up a second yellow card for handball shortly afterwards, and midfielder Joey Barton was forced to play as a lone centre-back.
"The sending off I can't defend, it's a red card but we had a choice to make, 'do we go for damage limitation or do we look to try and get something out of the game?' said Warburton, who conceded his side had conceded "poor" goals prior to that.
"That was a choice I made, no-one else, put on Harry, put on Waggy, be positive and try to get a second goal.
"Apologies to the support because they were magnificent. But at 3-1 that was my call to try to get something from the game."
Rangers manager Mark Warburton insists there is "no major gulf" between his side and Celtic despite a 5-1 rout in the first Old Firm derby of the season.