Hughton was axed by Brighton on Monday, despite keeping the struggling club in the Premier League and taking the Seagulls to the FA Cup semi-finals.
The decision has been widely criticised and was particularly condemned by anti-discrimination campaigners.
Moore was a surprise casualty earlier this season when he was sacked with the Baggies still in contention for promotion. They have gone on to secure a play-off place, although lost the first leg of their semi-final against Aston Villa.
The 45-year-old was sad to see his friend leave the Amex Stadium after bringing the club so much success, but he has strongly denied the suggestion that either of the decisions from West Brom or Brighton had anything to do with the colour of his and Hughton’s skin.
In fact, Moore told talkSPORT he understood the football reasons for both decisions and personally thanked West Brom for giving the opportunity to coach their team.
Speaking to talkSPORT Jim White on Tuesday, the coach said: “If you’re looking at myself and Chris, we’re still the same people as when we were offered the jobs, still the same people who these clubs gave the opportunity to manage.
“People may allude towards that [the apparently racial undertones] and I can’t change the mind set of people, all I can do is just speak on behalf of myself and when I got the job I was the same person as I am now.
“It was based on footballing matters and we move forward.
“We were installed in the jobs in the first place and I’d like to think that we’ll get opportunity to carry on being managers elsewhere. We’re both young managers in the game with bright and fresh ideas. We want to bring that somewhere else and have the opportunity at another club to get back into the competitive game, the game we both love and serve so well.
“Listen, Brighton want to go in a different direction and good luck to them, but we can’t take away from the sterling work Chris had done for that football club.