The visitors produced some impressive football during an entertaining first half at Dens Park.
Harry Forrester put Rangers ahead after 13 minutes before 36-year-old Kenny Miller added a second six minutes before the break.
But when the veteran frontman failed to beat Dundee goalkeeper Scott Bain moments later, that allowed Mark O’Hara to put the pressure back on as he headed home in the 44th minute.
The goal made the second half more uncomfortable that it should have been according to Warburton. But the Englishman was just relieved to see his men come through without suffering any more scares after last weekend’s opening day draw with Hamilton.
He said: “There was resilience, but we shouldn’t have to show resilience. I thought we were very, very good in the first half. We controlled the game and our movement was good. We created chance after chance and Lee Wallace was excellent on the left-hand side. We should have been more clinical, and then in the second half we shouldn’t have to show resilience. First half, it should have been game over. It could have been four or five with the chances we had.”
Dundee manager Paul Hartley was unhappy with the goals his side lost but picked out O’Hara for special mention.
The former Kilmarnock defender has been handed a more advanced midfield road since moving to Dundee this summer and Hartley believes he can help replace Greg Stewart following his move to Birmingham.
“I felt O’Hara was absolutely outstanding today,” Hartley said. “He showed what he can do at 20 years of age. His running power was superb. That was the pleasing thing for me, he gets his goal but his marking was excellent and he dominated the game second half.
“As soon as I spoke to him I wanted him playing central midfield pushing forward. I wasn’t interested in him playing right-back or in defence. We just changed his position a little bit and it just showed you. At 20 he can only get better. He has great energy, a great engine and he scores goals.”