Tempers flared on the touchline after Goodison's arm floored Bantams winger Kyel Reid in the first half.
Victory over last season's League Cup finalists, only their second of the campaign, moved Rovers off the bottom of League One.
Parkinson said: "As soon as it happened I was certain it was going to be red, but the fourth official said it was a forearm rather than an elbow - that is why it was a yellow rather than a red.
"My feeling was that it was a straight red."
The winning goal from Ryan Lowe in the 67th minute brought fourth-placed Bradford's eight-match unbeaten league run to an end.
Parkinson felt Tranmere had "come to slow the game down because they are scrapping for their lives".
He added: "They will feel they delivered a very professional performance, but they deliberately slowed the game down and were allowed to get away with it.
"This was a poor performance from the referee and the officials because they didn't do enough to negate Tranmere's spoiling tactics.
"We were disappointed with the goal we conceded. We got caught and that left Ryan Lowe with a clear shot."
- Sports & Recreation
- Ryan Lowe