Despite assuring reporters on Saturday that Oenning would be in charge for the Bundesliga match against Stuttgart this Friday, the Dane changed his mind 48 hours later.
Arnesen now says it was a mistake to give Oenning his backing following a 1-0 defeat to Borussia Monchengladbach and that the severance was necessary.
"After our games against Cologne and Bremen, I had a bit of hope, but Gladbach was disappointing," Arnesen told the Bild newspaper.
"After letting it sink in a bit, I analysed the situation again and it was up to me to decide whether Michael could still do it.
"I did not believe in it. You have got to be honest. I could not wait until Stuttgart."
Arnesen had been Oenning's strongest backer during a difficult first month of the season in which the club drew one game and lost five.
With their Bundesliga permanence under threat, Arnesen had to put his personal relationship to one side.
"I was fully convinced about my decision because it is the best thing for the club," he said.
"It is hugely disappointing because I had a very good relationship with Michael and he is a team player.
"It was ideal for me to work with him. Michael gave it everything, but in the end, it was not enough to turn the corner."
Arnesen must find somebody who can do that, with former Hamburg coach Huub Stevens among the likely contenders.
Stevens has been out of work since being released by Red Bull Salzburg towards the end of last season, and he has not hidden his desire to return to the north of Germany.
"I am free," Stevens told the Hamburger Morgenpost newspaper. "I had a wonderful time in Hamburg and have kept a piece of HSV [Hamburg] close to my heart."
Stevens faces competition from his fellow Dutchman Marco van Basten, whose agent Perry Overeem told the Welt newspaper that his client would be keen to hear from the club.
Overeem said: "Should Hamburg contact us, we would definitely listen to what they have got to say."
Rodolfo Cardoso has been placed in caretaker charge of the team.