Reds midfielder Jim O'Brien scored the only goal of the game at Oakwell, slotting home his third of the season in the fourth minute after collecting Martin Cranie's long ball and rounding Lions goalkeeper David Forde
Mellon said: "We know the value of three points at this time of the season and it was much-needed against one of the teams that are down there with us, so I'm delighted to get the result today and collect all three points.
"There was a lot of big performances there and it's those types of performances that are required at this time of the season and we're well aware of that."
Mellon said he was unconcerned by wins for the other two sides in the relegation zone, Yeovil and Charlton.
He added: "We're not good enough to think about anybody else; we've got to worry about what we do, concentrate on that.
"It won't affect us what anybody else does as long as we keep our part of the bargain and do the business.
"There're more teams than us in it, you've got to focus and concentrate on the very next half (of a match), break it down as much as that, and do well in it.
"It's tough; it's the Championship and anybody can beat anybody. We've just got to make sure we do the basics well and hopefully our big players turn up on the day and get results like today for us."