Two goals in the first half put the hosts in the ascendency, with Tom Pugh's red card compounding things for United, who had to play more than half the game with ten men.
"It was bad from start to finish wasn't it," Dean remarked. "Once the red card happened I feared the worst and that the floodgates could open up, such is the mentality we showed and intensity we played with against a side around us (in the table).
"It's embarrassing and I can only apologise to the fans on behalf of the players and myself for the last few performances because it's not been good enough. I'm livid really."
He added: "It was disconnected and when the ball came into the midfield areas we were five or ten yards off them. For the second goal, we switched off on a restart. They have multi-ball around the ground, which we worked on, but certainly used it to their advantage then - it was like they walked it into the goal.
"To be fair, they showed more fight and desire in the second half but it shouldn't take me going in there and shouting at them for them to come out and perform. Let's be honest, Gateshead also took their foot off the pedal."
See more from Jimmy Dean and Finley Shrimpton on Iron Player.
