The former Stockport and Motherwell boss has signed a deal until the end of the season after Cooper was axed on Monday after winning just one of his 13 games in charge and is under no illusions as to the size of the task at hand.
He said: "I see it as a fantastic challenge.
"I'm an optimist and a realist and I don't expect us to win 12 or 13 games but I am here to make a difference.
"I want to bring back some credibility and respect to the club and we need to start winning some games.
"I'm responsible for the next 18 games and I will work very hard to ensure that relegation does not hang over me.
"I am a long-term thinker but I am here to do a short-term job."
Chairman Darragh MacAnthony admitted on Tuesday morning the appointment of Kettering boss Cooper was a mistake but has banked on Gannon to pull off a miracle and keep the club in the division.
Gannon kept Stockport in the Football League in 2006 after taking over in similar circumstances and he believes a repeat performance is possible.
Gannon said: "Every club has its issues behind the scenes.
"There are always players who want to be somewhere else so I don't see anything untoward going on here.
"Team spirit has obviously been eroded over the last six months and the only way to get that back is by working hard and getting results.
"There is not one speech I can give that will make a difference but you'll be amazed how winning and getting clean sheets can make a difference and that is our first target.
"I took over at Stockport seven points adrift but we stayed up on the final day and it is possible.
"My initial concern is to get the best out of the players we have here and once they are giving their all then we can decide whether they are good enough."
Gannon's first challenge is at home to QPR on Saturday and he has promised to return Posh to the attacking football which saw them win back-to-back promotions under Ferguson.
He said: "I have strong principles about how football should be played but this club played good football under Darren Ferguson and I don't see why that can't continue.
"We will play in the right spirit and the right manner and I trust in the players to pick up results."
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