The pair, who were signed to replace the experienced outgoing duo of
were influential in the Warriors' Wembley win, with scrum-half Smith collecting the Lance Todd Trophy after being named as man of the match.
Stand-off Green, 26, also praised coaches Shaun Wane, Iestyn Harris and Paul Deacon for their assistance in helping the pair to settle in at Wigan, adding: "They have done a great job with us.
"They've given us plenty of confidence and we've worked really hard at our game. As satisfying as it is for Matty and I, they're a massive part of that result as well.
"We've still got lots of improvement to go, but in big games like that it's important you complete your sets, stay composed and kick well.
"In the wet conditions, that was the most important thing. We were never going to score lots of tries with the slippery ball."
Tomkins scores try in Challenge Cup win
Wigan's 16-0 victory at Wembley has given them the opportunity to become the first team since St Helens in 2006 to claim a league and cup double.
In a repeat of the Challenge Cup final, they host Hull in Super League on Friday before rounding off their regular season with a home fixture against reigning champions Leeds Rhinos.
Wigan are unable to retain their League Leaders' Shield, having slipped five points behind Huddersfield Giants with just two games to play, but will be among the favourites to reach the Grand Final at Old Trafford on 5 October.
"Knowing the type of bloke 'Waney' is, he'll be straight into us to make sure our heads are on for the play-offs," said Green.
"Hopefully the victory springboards us into the play-offs with plenty of confidence."
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