City have surprised the football world by taking two Premier League scalps - Wigan and Arsenal - to reach the Capital One Cup semi-finals, where they will face Aston Villa for a place at Wembley.
But Bradford are fifth in League Two, three points off the automatic promotion places, after their Boxing Day success over Stanley.
"We have banned all talk of our semi-final games against Aston Villa," Parkinson said.
"We want to go into those games against Villa in a good league position so we can enjoy them. The League Cup is great for the club's finances, but these games are our bread and butter."
Substitutes Alan Connell and Kyel Reid combined to win the game for Bradford with a smart goal four minutes from time.
The winner came seven minutes after 10-man Stanley had fought back to equalise through Benin international Rommy Boco.
Parkinson said: "It was tough out there with the rain and the heavy pitch and we scored our winner with a real moment of quality. It was a great cross from Kyel Reid and although Alan Connell made it look easy it wasn't an easy header. It was a great finish.
"It was a tough game. Accrington are a good side, they set their team up with a strong midfield and they are going to cause you problems with the way they play, but this was an important victory for us and we go into our next game at home to Rochdale on Saturday in good spirits."
Bradford deservedly went in front in the 24th minute courtesy of a goal from Garry Thompson.