Glen Jackson’s penalty left Tigers a point behind Sarries with just four minutes remaining of a pulsating game at Twickenham.
Club captain Murphy says Tigers refused to panic and it was their cool heads that helped set up the 33-27 win and a record ninth English league title.
“Four minutes is a long time in rugby, as it proved,” said Murphy, who collected his seventh league winners medal on Saturday. “We said we didn’t need to panic, we need to get up there, get the ball.
“If they had caught the kick-off and kicked it back to us, which they would probably have done, we had to hold onto possession and play through phases.
“Floody (Toby Flood) put a great kick in and Scotty (Scott Hamilton) has shown some great athleticism after 76 minutes to get to it and win the kick-off. He was smart enough to play Danny (Dan Hipkiss) in as well.
“It was great play by everyone involved and you are happy when you see someone like Danny coming off the bench.”
He added: “It was pretty tough. It was a physical game. I think it was a good standard of rugby played and we are delighted to get the win.”
Murphy paid tribute to the Tigers squad including teammate Lewis Moody, who made his final appearance for Tigers after 14 years and will join Bath Rugby next season.
"Lewis is a senior player, a fantastic player and he will be missed," said Murphy. "It's up to some of the younger guys to fill those big shoes.
"I am immensely proud. There are some very talented young guys and they are through and through Leicester guys. They are all club guys and passionate about the shirt and I think that showed.
"It comes down to the coal-face. We are very lucky to have a lot of guys who worked hard for the win."