The Bradford City manager brings his Bantams to Sixfields twice in the next couple of weeks, firstly for a League Two encounter in which the hosts will look to bounce back from an unexpected mauling at Underhill.
Parkinson was in attendance in North London and has warned his players not to take the result at face value.
"I have made it clear that Northampton could have been two or three goals up before Barnet took the lead," he said, quoted in the Yorkshire Post.
"Northampton are opponents who will be there or thereabouts in terms of the play-off places.
“They are a team who finish their chances and have two big men up front who we will have to handle.”