Slaven Bilic expected his sacking by West Ham after a poor start to a "crucial season" which club bosses believe can still lead to a top-10 finish in the Premier League.
Bilic, who was appointed in June 2015 on a three-year contract, was axed on Monday after Saturday's 4-1 loss to Liverpool left West Ham 18th in the table after 11 games.
Former Everton, Manchester United and Sunderland boss David Moyes is anticipated to be named as his successor - to become just the Hammers' 16th boss in 117 years. Moyes on Sunday expressed interest in replacing Bilic.
After finishing seventh in his first season and 11th last term, Bilic paid the price for a poor start to his third season as boss.
"I suspected it to be fair," Bilic told Sky Sports News as he left West Ham's training ground.
"We didn't start this crucial season well. We hoped that we could make that step (up) from the start and thought we could make it.
"Of course, you are always hoping and believing in yourself that you can turn it around and do it, otherwise you wouldn't be in this level.
"But it doesn't mean I don't understand the move that the club has made.
"No hard feelings. When I look back on my time, I am very proud of my work here."
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Slaven Bilic has confirmed that West Ham will offer Michail Antonio an improved contract this summer.
Antonio, who is set to return from a hamstring injury against Arsenal on Wednesday night, has been the Hammers' star performer this season and the club are determined to keep him in east London.
The 27-year-old England midfielder had already been tied down to a long-team deal, but the new terms will reportedly see his salary climb to £65,000 per week.
"The club and chairman appreciate the job he has done for us," Bilic said.
"The club is offering him a new contract definitely, for sure, this summer. He wants to stay. To be fair, he has a long contract anyway, it's not like he has one year left.
"But we appreciate what he has done and we want to keep him happy and keep him for a long time. The club are preparing for that."
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