The Spaniard replaced Arsene Wenger in the summer of 2018 but was axed as manager in November after a little over a season in charge at the Emirates.
Emery maintains he did a good job during his tenure, which included a run to the Europa League final last season.
“Arsenal was a club on a downward slope for two years before I arrived,” he told France Football.
“We stopped this fall and even began to rebuild the club with the Europa League final and 5th place in the league, only one point off of Tottenham despite the fact that we took just one point in our final five matches.
“We had Champions’ League qualification in our grasp and it went wrong in the end. But it was a good season and we had this notion of continuing to improve.”
Emery believes the loss of key players last summer contributed to the slow start that ultimately cost him his job.
“We lost our four captains: Koscielny, Cech, Ramsey and Monreal,” he added. “They were personalities that we missed this season to stay on the right track.
“And some stars did not have a good attitude and asked for more than what they were giving back.
“Taking all of that into account, we needed time to succeed with our transition to a new Arsenal which is what I wanted.”