The Tory MP, who was forced to quit as chief whip after an intense backlash following claims he called police officers protecting the Prime Minister "plebs", suggested No 10 "wanted this to go away" but said he could not live with knowing he had been "stitched up".
Mitchell believes he would still be in government if footage of the exchanges had been swiftly released. Cabinet Secretary Sir Jeremy Heywood, who viewed the tape in the days after the incident, was sharply criticised by MPs last month over his botched investigation.
The CCTV scenes threw into doubt police claims about what went on when the then Tory enforcer was refused exit through Downing Street's main gates on his bicycle.
But the footage only came to light after he faced a battle with officials to obtain his own copy of the tape.
Mitchell said he did not believe claims that the video could not be released on national security grounds were genuine.
"They really wanted me to lie low and let them get on with running the country but I couldn't do that - I couldn't wake up every morning for the rest of my life knowing that I had been stitched up."
Mitchell only asked to see the closed circuit footage of the altercation with police at the main gates of Downing Street on the day he resigned, October 19, but was not shown it for nearly three weeks.
"It was quite a frustrating experience," he said.
Mitchell was told he could not have a copy for national security reasons and it took almost a month before that decision was reversed.
"I do not think the arguments about national security were genuine, no," he told the programme.
He added: "I do not think that the release of the CCTV affects national security."
The Sutton Coldfield MP believes the footage, with a now disputed email purporting to be an eyewitness account of the event, would have quickly cleared his name if Downing Street had agreed to its release at the time.
"Well I think that, had the CCTV been released earlier, together with the email, I think that it would have been discovered quite early on that something was quite seriously wrong with this and I suppose, had that happened, I might still be in Government today."
Of suggestions Downing Street altered initial briefing notes to include the word pleb, he said: "I understand that two of the three poisonous phrases are in it, but whether there were two or three or one, whether it was done within one minute or an hour or three hours of the incident at the gate, it is wholly and totally untrue."
Four arrests have been made as part of the Operation Alice investigation into the incident. The row ignited when Mitchell was accused of a heated rant against officers as he left Downing Street on September 19.
Pressure intensified after The Daily Telegraph published a police log of the incident, which claimed he called officers "plebs" and swore at them repeatedly.
He insisted he did not use the words attributed to him and later said he was the victim of a deliberate attempt to "toxify" the Tories and ruin his career.
Prime Minister David Cameron repeated his desire earlier this week for a "thorough" inquiry into the Downing Street altercation.