Following back-to-back Yorkshire derby defeats, Parkinson's men travel to Ashton Gate to face a Bristol City side looking to stretch an unbeaten start to their league campaign to a club record 14 games.
Far from shy away from such a challenge, however, Parkinson says City must look to rise to the occasion and show the mental strength of the side.
Parkinson said: "We will be travelling down there and people will be expecting only one result.
"That is the sort of challenge you have to embrace and thrive on as a player and as a manager.
"We have had a tough week in terms of two defeats in our Yorkshire derbies but we have been in these situations before and we have responded.
"We need to regroup now and go again.
"We will need to show a resiliency about us, and that is something we will be thinking about when selecting our team. We need to go with the right team to give us a chance of achieving something from the game."