Johnson's delightful flick laid on the only goal for substitute Sergio Aguero in the closing stages to see City through to the last four.
And Johnson said: “It was a tough game, it's been a long week and a lot of travelling, but we've come away with the win and we're through to the semi-final.
“We changed the team around, it was the second-stringers if you like, but we're progressing as a team and as a club and I hope it continues.”
That progress has seen Johnson play only a fringe role for much of this season, but he said: “For me and the lads who are playing in this competition, it's a chance to try and get in the team week in, week out.
“And if we can get into the final and win another trophy, it's important for the club.”
Striker Edin Dzeko, who was also involved in the goal to cap an impressive display, added: “We played like a team, that's most important. I am trying to do my best every game and I think today was okay.”
Aguero was a first half replacement for the injured Aleksandar Kolarov, leading to a change of shape which appeared to benefit Dzeko.
And the Bosnia & Herzegovina frontman said: “We played from the beginning with one striker, with Sami (Nasri) behind me. Then Aleks got injured, Aguero got in and we played with two, for every striker it is easier with two.”
Nasri was not at his sparkling best against his former club, whose fans booed him relentlessly. And City boss Robert Mancini said: “That reaction is normal, when the supporters loved a player and that player comes back with another team, it is normal. Maybe it affected him."
Opposite number Arsene Wenger added: “You want players who have played for us respected.
“It is his first time back, I think it was more ‘disappointed love' than anger.
“I am sure they love him but because they love him, they responded like that — they wanted him here."
More impressive for the Gunners was young winger Alex Oxlade-Chamberlain, and Wenger is excited by the former Southampton man's potential.
"Chamberlain had an excellent performance," he said. "There is a big talent there, it looks as well as though he is not fazed by the occasion and can take the pressure he was under tonight.
"How much he wants it can decide how far he can go."
Former Gunners star Nasri’s first touch was resoundingly booed, before chants of "you only left for the money" rang out around Emirates Stadium.
City winger Adam Johnson's 25-yard effort dipped just over before Arsenal broke down the left through Oxlade-Chamberlain, who fed Marouane Chamakh before the ball was pushed out for Francis Coquelin to whip it back across the six-yard box.
Park Ju-young, who scored in the last round against Bolton, arrived on cue at the far post, only for reserve keeper Costel Pantilimon to make a brilliant reaction save to his left.
The 6ft 8in City keeper was called into action again on 27 minutes when the Romanian made another acrobatic one-handed stop to push away Oxlade-Chamberlain's fierce 20-yard strike which was heading for the top corner.
Arsenal were lively again at the start of the second half, as Oxlade-Chamberlain made more inroads down the right, this time an angled drive beaten away by the City keeper.
Edin Dzeko hooked Zabaleta's cross behind as the Blues maintained their threat before Koscielny made a couple of timely last-gasp tackles.
Seven minutes from time City broke quickly and this time produced a finish worthy of their multi-million pound attack to win the tie.
Dzeko's long ball split the Arsenal defence, before Johnson brilliantly played in Aguero — and the Argentinian coolly slotted past Lukasz Fabianski.
Arsenal sent on Russian playmaker Andrey Arshavin for Oxlade-Chamberlain in the closing stages as the home side searched for an equaliser, but there was to be no fightback.
It now seems that Arsenal will endure another season without a trophy.
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