Parkinson's men will go into this weekend's home encounter with Swindon having won five out of their last six games - a run that has included a trio of consecutive victories from City's last three games.
Despite the Bantams' excellent recent form though, City have had to battle hard for each of their last three victories, with all of the wins coming via a 1-0 scoreline.
Parkinson and assistant Steve Parkin were in the crowd on Tuesday night to see Swindon's 2-0 defeat at Oldham Athletic.
The Robins' loss at SportsDirect.com Park was the third in their last four games but Parkinson saw enough from the game to realise that City will be in for challenging fixture once again on Saturday.
The City chief said: "Swindon were obviously Play-Off finalists last season and could have been promoted. They haven't found the going as easy this campaign but they still have a strong side and we are expecting another tough match.
"Me and Steve (Parkin) went to their game at Oldham on Tuesday night and they looked in control for long periods of the match. We are wary of the challenge Swindon will present to us.
"They were without a few good players on Tuesday. Nathan Thompson will be back from suspension for them and maybe one or two others. We know we will have to maintain recent standards and keep playing well for this one.
"This Saturday is another crucial game and we'll be looking for the same intensity this Saturday that showed both on and off the pitch against Scunthorpe."
Rory McArdle put himself up for inclusion for the Swindon match after getting through 90 minutes of Tuesday's reserves match at Wigan Athletic unscathed. The match was McArdle's first since dislocating his shoulder at the beginning of last month.
Parkinson added: "Rory got a few knocks and challenges as you'd expect at centre half. But he came through it all fine and seemed to get more confident within himself as the match wore on.
"It was important for him and for us that he managed to get that game-time on Tuesday."