The 56-year-old has signed a deal until 2020 at the Hawthorns and will face Crystal Palace as his first game on Saturday.
The ex-Crystal Palace manager only won just six of his final 36 games until he was sacked in December.
He replaced Tony Pulis at Albion yesterday and he admitted that his axe at Palace still hurts.
“I did feel a little bit harshly done by on that decision,” he said.
“Of course you can justify it by saying on that particular run I had to go and that’s how the media is but sometimes as a manager with the relationship you have, I felt I had a bit more trust than that.
“But OK, now you get another go. I think it was important I got a club where I thought I could take it forward and an environment to give me a good chance. I was disappointed to lose my job at Palace, I really was.
“I think although we were on a difficult run, we had finished 10th, we had got to a cup final.
“I felt I deserved more time but I didn’t get it. I wanted to make sure when I went back in it was an opportunity with people I really felt comfortable with.”
He also answered misconceptions regarding his time as the manager of Newcastle.
“I think it’s a little bit unfair. When I left Newcastle people still came up, some Geordie fans, saying ‘we’re disappointed you got the sack’.
“I didn’t get the sack, I left, and when I did leave we were ninth.
“With the clubs I’ve managed you’re going to get difficult spells. I’ve not been fortunate enough to be at Arsenal or Liverpool where you can win 70-80% of your games.
“You’re going to have spells where you have to dig in and at times at Newcastle, Mike Ashley did very well for me, stuck by me in some difficult times.
“I’m open-minded, I still don’t think I’m perfect by any stretch of the imagination but I hope I’m a good manager for West Brom.”
With regards to his plans on West Brom, he said that he wants to place some excitement and challenge for trophies.
“My best teams play on the front foot. Sometimes they get a bloody nose doing that and that’s what I’ll deliver here at West Brom.
“And ultimately, hopefully along that line, we can get up to sort of 1.5 or 1.7 points a game. I’ve achieved that in the past at certain times at clubs and that’s what I hope to do here.
“I think the most important thing is, and it’s so difficult in the Premier League, to have ambitions to win the league, to win trophies, because you have six or seven clubs whose finances are way above the level that we’re working at.
“They all compete for every trophy, so even the League Cup now has become dominated by the top clubs.
“It’s very difficult to break. We almost did it of course with Palace in the FA Cup so you have to have those ambitions to try and win a trophy, as difficult as it is, and I think that’s the point I’m trying to make.
“I’ve come close twice, very, very close to winning the FA Cup, and one day I would like to do it. That’s the kind of ambition I’m talking about.”