Last month, Leicester recalled the 21-year-old from his season long loan spell with the Baggies.
And Moore has no hard feelings about the decision, expressing his joy at watching Barnes play against United.
"We are just delighted," said Moore ahead of his team's FA Cup replay with Brighton & Hove Albion on Wednesday night.
"When I saw him in the team against Manchester United it's the kind of things that dreams are made of.
"For us to to be able to give him the platform to perform, and he performed very, very well, just shows the levels he has grown in a short space of time.
"We should all feel proud here at West Brom giving him that development.
"And I'm sure he will be forever indebted to the football club."