Spurs' Europa League triumph was undoubtedly a major positive that could be drawn from an otherwise testing campaign last year.
The North Londoners finished 17th in the Premier League table under Australian head coach Postecoglou, who paid the price for Spurs' poor domestic form with his job.
Levy and the board of directors took the decision to sack the ex-Celtic boss, despite having ended Spurs' 17-year wait for a major trophy.
Daniel Levy: 'Spurs losing 22 league games is unacceptable'
Levy admits in a new episode of Sky Bet's 'The Overlap' that Postecoglou left the Tottenham Hotspur Stadium after writing his name into the club's history, but factors external to the manager's European victory ultimately informed his sacking.
"Ultimately, the decision sits with me, but it’s always a collective decision. We have a board of directors, but under the board, we have a group of technical staff, and they advise.
"We had to explain the decision to part ways with Ange. Ange just won us a trophy – a European trophy – highly significant and he’s always going to be in our history.
"However, we couldn’t lose sight of the fact that we finished 17th in the league, we lost 22 Premier League games, and it’s impossible for Tottenham to be in that position, and so we had to take the emotion out of it and we had to give some data points as to why we decided to do what we did.
“Whichever level you do it, no one likes telling somebody, ‘You’re losing your job’, but it is the nature of football. We’re there to win and yes, we won a European trophy – and it was fantastic – but we also need to win on all fronts – and the Premier League says it all," Levy said.
The Spurs chairman is regarded as an unpopular figure by supporters of the club and has held his current position for almost 25 years.
Levy is hopeful Spurs can get back to winning ways on the pitch, although that may prove difficult without talismanic skipper Son Heung-min who is expected to leave the club shortly, and midfielder James Maddison who was stretchered from the field during Tottenham's 1-1 pre-season friendly game with Newcastle United over the weekend.
“We will support him to the best of our ability," Levy said of new head coach Thomas Frank. "If you look at transfer fees, we’ve been in the top four spenders since the stadium opened, we’ve spent close to £700 million net on new players – this isn’t just about money. This is about some luck, having the right balance in the team, having the right coach – there’s a lot of things that have to come together.
“I very much hope that Thomas will bring all the right ingredients and bring this team to where it belongs, which is right at the top.”