The Bantams return to Valley Parade this weekend to continue their League 1 campaign after the midweek loss to Oldham Athletic in the Johnstone's Paint Trophy.
Opponents Yeovil will head into Saturday's encounter also off the back of a cup exit in the Johnstone's Paint Trophy following their 3-1 home defeat to League 2 side Portsmouth.
The loss was Yeovil's fourth of the season in all competitions, with the Glovers also recording only one win from their first seven league and cup matches this campaign.
Yeovil come into this Saturday's match three unbeaten in the league, however, and Parkinson is adamant City won't be fooled into taking the Somerset side lightly, despite their relatively slow start to the campaign.
Parkinson said: "Gary (Johnson, Yeovil Town manager) did an unbelievable job getting them into the Championship for last season and they made a good fist of staying up in the division.
"Gary is a very experienced manager and deservedly won manager of the year for League 1 the year he got Yeovil promoted.
"Coming down from the Championship last season, Yeovil have been tipped by many to go again this season (push for promotion) so we know Saturday will be tough.
"They have had a bit of a slow start to the season by their standards so they will be wanting to bounce back on Saturday - we have to be ready for that.
"We will have to be right at our best and ready to keep up the high standards we have set ourselves in this early part of the season.
"They have gone three unbeaten before Tuesday (JPT defeat to Portsmouth), and we won't be reading too much into that game because they made quite a few changes.
"We certainly won't be under-estimating them in the slightest because they are a team of players who were playing in a league higher last year."