The Magpies moved out of the bottom three after their 3-1 home win over Middlesbrough on Monday.
Newcastle have Fulham and Aston Villa left to play in the Premier League this season.
Guthrie 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.”