The Sports boss was impressed by his side’s weekend win over Boreham Wood, a result which took his team to fourth - two points off new National League South leaders Weston-super-Mare.
It’s fair to say the top of the division is littered with clubs not expected to put in a title challenge this season.
Above Eastbourne and sitting just below the Seagulls are Farnborough and Truro City.
Murray, a National League champion with Mansfield as a player and a North winner as manager of AFC Fylde, has seen enough to suggest his team have nothing to fear.
“This league is all about us,” said the former midfielder, who replaced Mark Beard at Priory Lane in early January.
“We know there are some really good teams but I don’t fear anything in this division.
“My group of players have a lot of quality but I have asked about mentality from them - I want that belief in what we do. Saturday they showed it.”
The 2-1 win over fancied Wood, managed again by club legend Luke Garrard, saw them come from behind.
Five teams have topped the table since the end of August and Murray feels there’s a chance the Sports can stick around.
“I would say it’s probably the best result of the season so far,” he said after the weekend win.
“We’re trying to demand more from the players, asking them to be that little bit more ruthless. I honestly believe we can put anyone to the sword.
“For me Saturday was a big tick in the box. It was a fantastic result.”