The holders enjoyed the vast majority of the chances but could not find a way past the inspired David de Gea and went behind to United’s first attempt on goal 10 minutes before half-time when Nemanja Matic fired home.
United’s hopes of completing a miraculous comeback were extinguished when Matic was then sent-off 15 minutes from time and City held on to face Aston Villa at Wembley on March 1.
“In 180 minutes we were better than United,” said Guardiola. “We created chances to score a lot of goals and didn’t convert. We need to learn to be more clinical.”
City started like they did in racing into a 3-0 lead within 38 minutes of the first leg at Old Trafford as they swarmed all over the visitors, who had De Gea to thank for keeping them in the tie.
“I can’t really comprehend how we lost this game,” said City midfielder Kevin de Bruyne. “I think we got sloppy.
“For me Manchester United didn’t have one chance today.”
Sergio Aguero was first to threaten with a diving header that the Spaniard parried to safety before using his legs to repel Riyad Mahrez’s effort.
Bernardo Silva flashed a shot across goal before more De Gea acrobatics denied Aguero again at his near post.
United had not even mustered a shot in anger for the first 35 minutes, but suddenly the tie was back in the balance when Matic connected sweetly from the edge of the box after City failed to clear a free-kick into the box.
The hosts did have the ball in the net before half-time when Raheem Sterling finished off a flowing team move, but the England international was denied his first ever goal against United by an offside flag.
Sterling contrived to miss another glorious chance to kill the tie off just before the hour mark as he rounded De Gea but blasted over with just defenders on the line to beat.
Guardiola then could not believe his eyes when David Silva tried to tee up Ilkay Gundogan rather than shoot with just De Gea to beat after Harry Maguire was caught in possession.
The tension among the home support was eased when Matic finally paid for persistent fouling when he chopped down Ilkay Gundogan to cut short a City counter-attack.
“It’s hard to go here and score a goal with 11, nevermind 10,” said United boss Ole Gunnar Solskjaer. “It’s never a sending off for me – it’s a joke.”
Aguero finally beat De Gea with a deft finish only to also be flagged offside in the closing stages as United salvaged some pride, if not their chances of a first trophy since 2017.
“I’m so proud of these players,” added Solskjaer. “They’ve beaten City now twice at their place. They’ve given us everything.”
United executive vice-chairman Ed Woodward has not been present at recent games as animosity towards his part in the club’s declining fortunes on the field has grown.
However, Woodward was in attendance at the Etihad just a day after a hooded mob attacked his home with flares and graffiti.
