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Arsenal were 4-0 down but took the game to extra-time, with a Theo Walcott hat-trick and two Marouane Chamakh goals helping them into the last eight.
"We went from disaster to rescuing some pride," Wenger said. "You cannot play for Arsenal and give up."
Reading boss Brian McDermott said the defeat was the "worst" of his career.
Arsenal found themselves 4-0 down after 35 minutes but Walcott made it 4-1 just before half-time to set up the platform for an incredible second-half revival that took the game into extra time.
Chamakh put Arsenal in front for the first time on the night with a goal in the first period of extra time, only for Reading striker Pavel Pogrebnyak to make it 5-5. But Walcott restored Arsenal's lead before Chamakh scored their seventh.
"It was 4-0 and could have been one or two more," Wenger added. "We came back but at 89 minutes it was still 4-2. Then the miracle happened. There were so many turning points. Our first goal before half-time was important. It's my first 7-5. It was a tennis score."
Wenger said he knew the pain of relinquishing a four-goal advantage, having drawn 4-4 with Newcastle after being 4-0 up in February 2011. He explained that his team had drawn inspiration from their supporters.
He said: "I know how it feels to lose a 4-0 lead - it happened to me at Newcastle. I always hoped we could come back. It's strange to explain. At 4-0 you think you have won the game, but at 4-2 the panic starts to set in.
"At 4-0 I didn't feel great, I started to think about half-time. Inspiration was not difficult. I just felt sorry for the fans, they stuck with us. A big part stayed and supported us and I give them credit. I give the ones who left less credit.
Premier League, Newcastle 4-4 Arsenal, 5 February, 2011
Arsenal led 3-0 inside 10 minutes at St James' Park and 4-0 at half-time but were pegged back with Cheick Tiote's stunning late volley capping the comeback.
Champions League final, Liverpool 3-3 AC Milan, 25 May, 2005
Liverpool were down and out after going into half-time 3-0 down but scored three times in six minutes to turn the game on its head.
FA Cup fourth round, Tottenham 3-4 Manchester City, 4 February, 2004.
Spurs were 3-0 ahead at half-time before Joey Barton was sent off. But somehow City fought back and Jon Macken scored a dramatic late winner.
Premier League, Tottenham 3-5 Manchester United, 29 September 2001.
Again Spurs went in at half-time 3-0 ahead but were ripped apart in the second half by a breathtaking United performance.
FA Cup final, Blackpool 4-3 Bolton, Wembley, 2 May, 1953.
Bolton had led 3-1 and, were still leading with three minutes to go until Stan Mortensen and Bill Perry struck.
"This was maybe my greatest comeback. [The League Cup] is not my priority but had we gone out like we could have gone out it would not have been one of my proudest nights."
Reading boss Brian McDermott described the defeat as the worst of his career and identified Arsenal's first goal before half-time as the turning point.
"I wasn't happy at half-time because we went in at 4-1 instead of 4-0," he said.
"That gave them impetus they didn't need. We'd dominated the first half and then they scored a goal out of nothing.
"When you give good players and teams a lift like that, they take the chance. It was kamikaze football in the second half and extra time. Even at 5-5 it's extraordinary. It's the worst defeat of my career."
McDermott was angry that Walcott's equalising goal arrived almost two minutes after the minimum four minutes of stoppage-time had been played.
"Obviously it doesn't help that the referee added two minutes on to the four minutes of injury time to make it six," he said. "You can't tell the time as wrong as that, but he did.
"At full-time nothing needed to be said to the players. Sometimes the less said the better. We know what happened.
"This game will be remembered for a long time and that makes me feel a whole lot worse."
Arsene Wenger says Arsenal's recovery in their incredible 7-5 victory over Reading in the Capital One Cup took them from "disaster to pride" .