The Galway outfit know that a win away to play-off chasing Glasgow Warriors would secure eighth place in the league, to add to the Heineken Cup qualification secured by virtue of the all-Irish European final at the end of the month.
And having won their last three RaboDirect PRO12 games, Murphy is desperate to make it four on the bounce for the first time since 2002.
"Connacht is very different to where I have been before, everyone knows each other over here and I really like the atmosphere," said Murphy, who signed a contract extension until the end of next season.
"It's going to be my fourth season next year which shows how much I am enjoying it here.
"The club has changed massively just in the time I have been here, and we are becoming more and more competitive.
"Whereas teams used to not like coming to the Sportsground because of the conditions, now I think it's a case of them not looking forward to playing us.
"We've had a lot of work done on the Sportsground and that was a massive boost for the club this season.
"We're on a good run at the moment but we really want to make it four wins in a row.
"It's important heading into next season to finish on a high this year."
Connacht's winning streak nearly came crashing to a halt ten days ago when Aironi looked set for a first-ever away victory only for the home side to stage a late fightback.
And Murphy, who was replaced ten minutes from time, admits he found it difficult watching from the sidelines.
He added: "It was an extremely strange game. We thought we were in good form going into it and were hoping for the win but it didn't seem to be working for us.
"It was tough having to sit on the bench at the end but it was an incredible comeback for us.
"We had a little sticky run earlier this season but we didn't feel we were playing too poorly, the results just weren't quite coming.
"Now we've managed to pick up a few wins so we have to build on that against Glasgow."
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