Kyel Reid had given City a first-half lead but a Nathan Doyle own goal levelled the tie and Clayton headed home before Bradden Inman and Chuks Aneke netted late on to put the result beyond doubt and book their ticket to the Johnstone's Paint Trophy Northern Section final.
After Tuesday night's victory, Davis said: "It was good for Max to score for his confidence. He's a good player but he is only 18 and it has been a bit of a struggle for him lately so I'm delighted for him to come on and make an impact.
"I was delighted with the result but I wasn't over impressed with the performance although cup games are about winning.
"We managed to do that convincingly in the end but I have to admit I don't think we deserved to win by the margin we did.
"Our first-half performances haven't been up to standard off late and for some reason we don't get ourselves going until I have spoken to them at the break."