Moyes is believed to have given Davey help with his preparation for the trip to Anfield and Swansea-born Davey said: "I owe David Moyes a lot.
"My career was ended when I was 27 after a back injury. David gave me the job running the youth team, and I will always be grateful.
"When your career ends like that you worry about where the next pay cheque is coming from, and I will always be thankful for what David Moyes did for me.
"I went on to take my coaching badges and now here I am with a side one step away from the FA Cup semi-finals, which will be played at Wembley this season."
He said: "I looked at the sheet and saw that Gerrard, Fernando Torres and Jose Reina were not involved. I accept that they have top stars to come in, but when I put the names of their players up on the board before the game I felt we had a chance, it gave us hope."
And Davey explained the Tykes' tactics, saying: "We made sure we stopped the supply up to Peter Crouch, and got into their faces.
"We played Crouch well all day and then our centre-half Stephen Foster managed to get above him at the other end to head home our equaliser."