Mclean, who joined the Bantams from Hull in January after the club sold Nahki Wells to Yorkshire neighbours Huddersfield, broke his duck at the 11th time of asking.
However, the visitors hit back with a Cody McDonald goal to earn a point in a mid-table battle that leaves both clubs who won promotion from League Two last season level on the same number of points.
Mclean was expected to fill the gap left by Wells' departure, but nothing had gone right for him near goal until Saturday afternoon.
Bradford boss Parkinson said: "I think Aaron's performances have deserved that goal. The good thing about him is that the longer he has been here the harder he has worked.
"Supporters have been patient with him because they have seen he has done everything possible to get a goal
"He played tremendously well in our 2-0 win at Colchester in midweek and he has got his reward by scoring a text book goal, a great team goal, a fantastic run and good connection.
"If you talk too much to a striker about goals it creates pressure, but I say to him keep playing well so that we win games of football - that is what he has got to do.
"The most important thing is that we get points and if we can't get three then we get one. If he scores goals great, but his performances have been good."
Parkinson added: "This is two points dropped. With the amount of pressure we have had and the possession we enjoyed we dominated the game. Gillingham didn't threaten and yet they have nicked a point off us, but Cody McDonald is a goal scorer and he also scored against us here last season.
"The defence are not pleased with themselves. Mistakes were made on the halfway line, but we should have been able to rectify them. Yet, we played so much good stuff and to take 10 points from our last six games is a tremendous return.
"We set ourselves up to take all three points but, although we didn't do that, I am pleased with so many aspects of our performance."
- Sports & Recreation
- Phil Parkinson
- Adam Drury