Yeovil got off to the best possible start when they took the lead in the 10th minute, with their first meaningful attack. Joel Grant got on to the end of a cross from the right and from 12 yards out he slid the ball into the empty net.
However, Marcus Tudgay's penalty, after referee Lee Probert ruled Tomasz Cywka had been tripped, earned Mellon his first point at Oakwell.
Mellon said: "It's hard enough to win matches but when you gift goals like that it makes it even harder.
Both teams were a bit nervy but I cannot fault the effort of our lads.
"From where I was it was a definite penalty, without a shadow of a doubt. Cywka is a dancer when he gets the ball in the area and the only way to get him of it is to foul him.
"They found a way to get back in the game and then we had a real go at trying to win the game.
"I think it's a case of two points lost, I think we tried everything we could to get the win."
In the 67th minute Yeovil thought they had retaken the lead when Ishmael Miller bundled in a Joe Grant cross from close range - but Probert ruled that the striker had handled the ball.
Commenting on the disallowed goal, Mellon said: "It was a handball, he punched it into the net and we are playing football not netball."
Yeovil boss Gary Johnson said: "I thought both teams tried to get the ball down and play football and both tried to win the game. It was a big game for both sides.
"We had one or two opportunities where we should have scored. We are disappointed that we are not going away with three points after the effort we put in.
"I am not going to comment on whether it was handball until I've looked at it again. I want to look at it again or I might make myself look silly.
"Who knows what handball is now? None of us know what handball is. He was a yard from goal so why would he handle it? We thought the penalty that was given was a bit soft."