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The Bulls ended the Mariners’ 16-game unbeaten run thanks to two stunning second-half goals from Harrison Sohna, securing a third straight league win and continuing the remarkable start to Downes’ reign.
Going into the game after a 5-1 win over basement club Leamington on Tuesday, the Bulls' gaffer told the players that while that was about what they did on the ball, today was about what they did off the ball.
"You're going to have to sacrifice," he said. "You're going to have to remove your ego.
"You're going to have to be very humble because to run so hard and to work so hard and to sacrifice yourself takes humility.
"It does take people to remove that ego and go 'okay, I'm happy to do it'."
He added: "I'm ever so proud of them in that sense because no matter how you set up tactically, if you tell them to do this, that and the other from a tactical point of view, if they're not going to do it from a physical or mentality point of view, then it's pointless.
"That's what is really, really important. Work rate was incredible throughout the game."Hereford were required to soak up long spells of pressure from the league leaders, particularly in the closing stages after Lennon Wheldon pulled a goal back deep into stoppage time.
The victory means Downes has now overseen five wins and a draw in his first seven matches in charge since arriving at Edgar Street.
"It's a great result for us, definitely, it's a good win," he told BBC Hereford and Worcester's Carson Wishart.
"They're a difficult team to play against, make no bones about that. Don't get me wrong, I'm delighted, I'm very happy with the result.
"I do go back to the players because they absolutely ran their socks off today."