The 43-year-old Spaniard, who said in April he would leave the club at the end of the season after taking charge in 2023, oversaw a dramatic rise that culminated in Bournemouth's best-ever Premier League finish.
"I am quite hard but I have been really close (to tears). I cannot ask for much more," Iraola told BBC Sport.
"I have been so lucky to be in this moment with this group of players with this club. I think it is the perfect ending and I am so thankful."
Bournemouth, who were in the third tier of English football 13 years ago, will play in Europe for the first time in their history.
Iraola said securing European qualification had not been part of his initial expectations, as his primary focus was to reshape the team's style of play.
"I had no idea (about reaching Europe when joining)," he said.
"The first thing from the club was more than the results, changing the style, changing the approach, being more offensive and proactive – that's why they signed me. The club was focused on this and this is why I was attracted to the idea.
"I knew it was almost impossible to get Europe but the owner told me since the beginning, 'I want Europe.' To finish the three seasons giving back, not just to the owner but the fans and players, it is one way of thanking them."
Bournemouth closed the season with 57 points, winning 13 of their 38 matches.