An epic encounter which ended 2-2 after extra-time brought the most dramatic of endings, with Hoops substitute Tom Rogic firing his spot-kick over the bar to see the Ladbrokes Championship title winners through to the final against fellow second-tier side Hibernian next month with a 5-4 win.
Celtic, on their way to their fifth consecutive Premiership title, were heavy favourites going into the game.]
Ronny Deila's side had comfortably beat Rangers 2-0 in their League Cup semi-final last season and this time an already thin Rangers squad was missing four players for differing reasons, with only five substitutes named.
Warburton said: "The favourites had to be Celtic. Anyone who understands football will say they have the stronger squad, they have the experience and they were the favourites and I can understand this.
"I was irritated by people underestimating Rangers.
"I read reports about them getting battered by Celtic today. Well they showed today that they've got quality, they've got the commitment and the work ethic and that gap is a lot, lot narrower than people are talking about.
"We've been good this season. We're not clear in the league by 17 points by chance.
"We deserve to be and the young squad has come together quickly so all credit to the players.
"I think they deserved a little more respect.
"I'm just delighted for the fans. The level of support they've given us again was magnificent.
"They've been in some dark places over the last four or five years, so it's tremendous that they can enjoy days like today and last week.
"We were down to the bare minimum with 16 players and young Liam Burt on the bench, but I thought to a man they were outstanding today.
"I thought we deserved to win the game of football. That's the most pleasing thing.
"Our message before the game was do what you've done all season just do it better against the number one team in the country and I think we did that today."
Barrie McKay impressed for Rangers
Image credit: PA Sport
A first-half goal from Gers striker Kenny Miller was cancelled out by Celtic defender Erik Sviatchenko's header, with Rogic equalising Barrie McKay's wonder strike in extra time.
Andy Halliday, McKay, Lee Wallace, substitute Gedion Zelalem scored their penalties for Rangers, while James Tavernier fired his over and substitute Nicky Clark had his saved by Craig Gordon.
For Celtic, Charlie Mulgrew, Nir Bitton, Leigh Griffiths and Mikael Lustig scored, with substitute Callum McGregor hitting the bar and Wes Foderingham saving from skipper Scott Brown, before Rogic went from hero to villain.
Celtic boss Ronny Deila insists he was dealing with too many emotions to think about his future, which has been subject to the sort of speculation that will increase following the defeat to the Ibrox men.
The Norwegian described the match as "rollercoaster of a football game, up and down and in the end very down", but was in no mood to look any further than Celtic's next league game against Ross County.
"After this game it is hard to talk about those things," he said.
"There is a lot of emotions going on, but with bad results you of course get the questions.
"You know you are going to get that pressure all the time when you don't get the results you wanted.
"I know why the question is coming, now we have to lift ourselves after that disappointment and get the league over the line.
"Of course I am disappointed that we lost the game, having said that I am not very satisfied with the performance either.
"We had to be quicker and calmer on the ball and play our game, the positive is that we came back twice and created some chances but overall, not the best day we have had."
There was an air of defiance in Deila's response to the question of whether Rangers can mount a serious challenge for the title next season.
"We are going to be ready when they come up," he said.
"Now we are top of the league and we are going to fight to get that title to Celtic Park.
"We will see next year what they have to offer.
"It is a totally different thing to do something over 38 games than to do it over one."
Rangers celebrate the moment they beat Celtic on penalty
Image credit: Reuters