Rovers came through the test with flying colours as they won 3-1 at the Shay.
Mellon knew it was one of the most difficult draws possible and was thrilled his team found their goal touch after being barren in the Vanarama National League.
Being one of the division's less lethal sides, they didn't find goals hard to come by in Yorkshire.
"We were really professional - we knew how tough it would be coming here but we played very well," said the manager.
"We eventually took our chances which is something of course which hasn't been our strong point so far this season.
"The second half was more like what we had worked on in training. There is always stuff we want to get better at but we played very well.
"I'm pleased for the lads getting through to the next round of the FA Cup because it's a completion that means a lot to the everyone."