Murphy paid tribute to his side's second-half display as they equalised just after the restart before grabbing the winner in stoppage-time.
"At half-time we felt that if we went out and started at a very good tempo then we might just surprise them a little bit.
"If we hadn't got anything in the first five minutes then we would have settled down then and played."
The match marked first goals of the season for Joe Skarz and Michael Collins, both products of the club's youth academy.
Murphy said: "Michael hasn't played a lot this time and I thought he worked very well today; I thought Joe did - I thought they all did.
"James Berrett went in the middle of the two centre-backs and I thought he was a giant in there today - he was fantastic.
"We needed it badly - I felt that if we didn't put a show on for the fans then they would have had their justification in having a go at us.
"The most important thing today was effort, commitment and trying to win the game and I think they did all those things."
Our ambitions are still the same - we're looking to get promoted from this league
Huddersfield midfielder Michael Collins
Collins' goal was his first of the season, and he called on his side to build on the victory.
The 22-year-old said: "We deserved the break because we've been playing some good stuff all season and it's just not been happening.
"Today is even better because it happened at Leeds United but it'll go to waste if we don't use it now as a spur for our season because our ambitions are still the same - we're looking to get promoted from this league.
"Hopefully today will be the catalyst to get us there because everyone concerned - the chairman, the fans, obviously the players - we're all striving for the same thing."
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