On a goalless afternoon, the hosts' best chance fell to midfield player David Syers in the 67th minute. Winger Will Atkinson played him through on goal, but his shot lacked power and Wes Foderingham saved.
Parkinson's side have struggled against relegation for most of the season and only confirmed their Football League status a fortnight ago
The Bantams boss said: "This club has a great history and tradition and it would have been a travesty if we had been relegated. We have got to make sure we are not in that position again. The only way we can stop that happening is to make sure we keep the players we want to keep and bring in some more.
"When I was appointed Bradford City manager last September, one of the reasons I wanted to come here was that I knew if I could get this club going the sky was the limit. That is why it is a good job and I am relishing the challenge.
"You normally feel drained at the end of the season, but I feel ready to go and I am looking forward to next season, to the challenge of building a squad and to make sure we don't feel the pressure we have felt this season. I want the pressure, but I want the pressure of challenging in the top half of the table not the bottom."