The Magpies climbed out of the bottom three on goal difference on Monday night with a crucial 3-1 home triumph over fellow strugglers Middlesbrough.
It was the first victory of Alan Shearer's reign in his sixth game in charge, with a home date against Fulham next on the agenda followed by a final-day trip to Aston Villa.
And midfielder Guthrie knows the St James' Park outfit must remain focused on the visit of the Cottagers on Saturday if they are to preserve their top-flight status.
Massive gameGuthrie said: "It was the most important result of my career.
"But we can't get too carried away because we have another massive game against Fulham to concentrate on.
"The biggest mistake we could make is to think we are already safe.
"We haven't achieved anything yet."