The Welsh had been 13-0 down after a Conor Murray try and two penalties from Jonathan Sexton.
But despite losing Ospreys' Dan Biggar to an ankle injury early on, Taulupe Faletau's try and the boot of Rhys Priestland got the visitors back into contention.
They then went 16-13 ahead but another penalty for Sexton ensured it would be honours even, leaving a sour taste in Warburton's mouth.
"It takes away a potential Grand Slam, a potential Triple Crown and it means we will need another big scalp down the line to try and win the Championship," he said.
"The positive is we managed to pull it back, even with losing Dan (Biggar), I thought Rhys came on and played his part, he got plenty of points for us.
"The good thing is this was one of our away games - of our next four games, three of them are at home.
"That's why we were so desperate to win here because it sets you up for the tournament.
"I am pleased with the way we weathered that storm, 13 points behind to pull back. Two years ago we didn't do that and it was one of the worst international games I have been involved in."
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