Parkinson, whose two-year contract at Valley Parade is up at the end of the season, is in talks with the club's board about a new deal and turned down the chance of becoming Blackpool's manager on Thursday night following the departure from Bloomfield Road of Michael Appleton.
The 45-year-old said: "I'm happy here. Bradford is a really good club with a lot of potential to keep improving and that's it."
Parkinson added: "I didn't want to detract from the contract talks and what we are trying to do here. That is in the background and will take care of itself."
The Bradford boss was speaking after his side were brought back down to earth by Oxford with a last-minute penalty four days after beating Aston Villa at home in the Capital One Cup semi-final first leg.
Lancashire referee Jeremy Simpson judged that right-back Stephen Darby had tripped Alfie Potter in the box and Peter Leven scored from the spot, but Parkinson had doubts about the decision.
He said: "My first impression was that it was a poor decision, but I'm going to have another look at it.
"I thought the referee was poor all the game. I suppose you are spoiled when you get Howard Webb on Tuesday (for the Villa match) and you get the officials we had here. They were below-par and they lacked an understanding of the game.
"It was a scrappy game. We just felt as soon as we saw their team and the conditions it was going to be one of those of kind of days when you have to grind out a result and we almost did that.
"It is disappointing because we wanted to give our supporters another display to keep us up there, but we haven't done that and that is the highs and lows of football."
- Sports & Recreation