Appleton admits he's spoken with Di Matteo and Eddie Newton since their dismissal.
He told the WBA website: "It was a situation where I felt I had a responsibility to the players more than anything.
"I was more than happy to do that. The next step was to call Robbie, Eddie an Ade to have a frank conversation and talk about how disappointed they must be.
"And what I would say is all three of them were very disappointed but philosophical about the situation.
"We're in a little bit of a dogfight.
"Obviously, results-wise over the last 18 games it hasn't been fantastic. But one thing they were very clear on is the fact they wouldn't want anyone else to take charge - especially for the game on Saturday.
"They all wished me the best for Saturday and I thought that was quite nice because it's not an easy situation for them to be in.
"They told me I have their full backing."