They have since gone unbeaten in the past six matches in the league, managing two wins and four draws.
As they prepare to take on the Cherries, Hasenhuttl said of O'Neil to reporters: “Absolutely an incredible job. I know how tough it is to stay unbeaten in the Premier League.
“He took everything from the bottom if you want. I know how it feels when you lose high and then have to turn things around.
“He didn't lose that high – he was immediately following and had the chance to build up a team.
“I think you could see that he found immediately a very successful way of playing football with a very clear, demanding shape – clear automatism, what is for me always a sign of a manager who knows what he does and brings in immediately what is necessary.
“This is very impressive to watch."