The former England manager was given his marching orders on Wednesday, six months into a two-year deal that will reportedly earn him £11m in wages and compensation.
Everton's board felt that Allardyce's position had become untenable due to supporter unrest, with a number of protests being held in recent weeks by the disgruntled fanbase.
Twenty-four hours on from his dismissal, however, the 63-year-old says that he bows out with his head held high after stabilising the Toffees on the field, even if the style of play was not to everyone's taste.
"I would say most of the Everton fans didn't want me out... the fans who show discontent are always more vocal," he told talkSPORT. "The club was in a very difficult position, but it improved as time went on. If it wasn't enough for the Everton fans at that time who were showing some discontent, I think there were certainly more fans who were happy with what we were doing than the ones that weren't.
"Yes, some of the football could have been better. I agree with that and there's no doubt about that. We all want to try and create as much entertainment value and results as much as we can... but you are left with the tools you have. When I came it was all about reorganising Everton, because of the huge amount of goals they had conceded before I got there.
"The satisfying thing for me was the response of the players and the staff on the position we finished. I enjoyed the time I had at Everton. It wasn't long enough, but there we go. I was surprised how it came about. It seemed to be done and dusted through the media before I met Farhad [Moshiri, Everton's majority shareholder]. I think it was out there in the open for a couple of days. That leaves you with the certainty of what was going to happen and I prepared myself.
"It was slightly disappointing. Who was involved in that I couldn't tell you, but something as delicate as that is something you want to be confidential. My meeting with Farhad was amicable. We conducted ourselves amicably but I expressed a disappointment with how it got out. I accept it and move on. I was not employed to do a short-term job on this occasion and that was the reason I came back. But in the end, for whatever reason, it wasn't enough and I accept that. I don't hold any grudges."