Fraser Preston (two), Luke Shiels and Danny Elliott found the net as the Pilgrims built on Tuesday's 3-0 win over Farsley Celtic to round off a great first week in the job for the new manager.
"I think the players deserve the accolades," Cox said.
"They've worked hard out there, there's probably a few tired legs getting up to 60-70 minutes as we worked them pretty hard on Thursday night even after a tough Tuesday.
"But they dug in. We know we've got good players, but what I want to see is the other side, the horrible side of the game and we did that and worked hard.
"On a horrible day with swirly horrible wind it makes the game unpredictable, but we've shown we can battle and grind out a result in tough conditions.
"That pleases me more than Tuesday night. I saw a different side to the squad and we did the things that win you games - one or two threw bodies on the line and others worked over what was expected because they wanted to keep a clean sheet."
Cox also praised the fans for getting behind his side this afternoon.
He added: "They got 100 per cent behind us all through the game, it's what this club's capable of home and away.
"We know there's great support here. All we've got to do is our little bit and if we do they'll get behind the players in droves.
"What they've seen is lads working hard for the cause and there's one or two who sacrificed themselves today with unselfish running."
MORE PILGRIMS: United 4 Chester 0 - report