Scott Williams crossed for the only try of the game to secure victory for Wales, who battled back from 12-6 behind.
"We didn't play well at all today [Saturday]," man-of-the-match Warburton said on BBC1.
"We knew it was going to be our toughest game so far, knew England are a quality outfit and flipping heck that was one hell of a Test match.
"To get the triple crown is unbelievable."
The win was Wales' third in a row and kept them on course for the Grand Slam, but Warburton said the squad are not getting ahead of themselves.
"I'm not going to jinx myself, I'm not going to say it (Grand Slam)," he added on BBC1.
"We've got Italy now at home in two weeks and that's a must-win game for us. We can't really look any more than one game ahead."
Williams came off the bench to settle the game and hailed the Welsh defence for standing firm when they had Rhys Priestland sin-binned in the second half.
"I never would have thought that (I would score the winning try), but it's happened and it's quite unbelievable really," he said on BBC1.
"I thought our defence was superb today [Saturday]. England threw everything at us, it was tough, but we stuck in there and managed to get the win."
His team-mate Ken Owens added: "When we went down to 14 men we just kept playing and kept believing and got that bit of luck with Scott."