Wales made 250 tackles as they ended Irish hopes of a Grand Slam and kept their Six Nations title hopes alive.
Warburton, 26, who led Wales for a record 34th time, said the huge defensive effort was key.
"It's probably the most exhausted I've ever been in an international match," he said.
"The reason we made so many tackles was that Ireland kept the ball extremely well, particularly in the second half."
Man-of-the-match Warburton was sin-binned in the first half but Ireland only managed to score six points to Wales' three in the 10 minutes he was off the pitch.
Trailing 15-9 early in the second half, Joe Schmidt's side went through 32 phases of play in or near the Welsh 22, but were unable to find a way through the resilient Welsh defence.
Wales sparked into life as an attacking force following the Irish onslaught and replacement centre Scott Williams made the breakthrough as he feigned a pass and dived over to give Wales a 20-9 lead.
Ireland fought back and won a penalty try after Wales were judged by referee Wayne Barnes to have illegally brought down a rolling maul from a driving line-out.
A Leigh Halfpenny penalty eased Welsh nerves to put Warren Gatland's side 23-16 in front, but Wales were forced to defend heroically once more in the closing stages as centre Jonathan Davies was sin-binned with only two minutes left.
"The attitude and defensive effort was second to none," said Warburton.
"Shaun [Edwards, the Wales defence coach] has gone into a lot of detail all week about certain [Irish] plays we would have to cover, their trick plays and what they do in attack.
"Credit to the boys, they took on all that information."
|Team||Points difference||Final-day match|
|The three-way battle - who needs what?|
Wales' win over Ireland and England's victory over Scotland means there will be a three-way race for the Six Nations title on the final weekend.
England, Ireland and Wales are locked on six points with three wins, and England's points difference of 37 puts them top, ahead of Ireland's 33 and Wales' 12.
Wales are in action first on Saturday 21 March away to Italy, Scotland then host Ireland, with England rounding off the tournament against France at Twickenham.
Warburton said the victory over the Irish was one of the best wins he has had.
"That's as satisfying as the win we had against South Africa in the autumn, England in 2013 [to win the triple crown], and then probably the world cup quarter-final in 2011 against Ireland," said the Cardiff Blues flanker.
"Because Ireland are that good. They won 10 games in a row, they are third in the world and I know it was probably going to take one of our best performances that we've had to get a win today.
"It's probably one of the best feelings I've ever had in a Wales shirt."