Flitcroft was appointed at Gigg Lane earlier this week following his sacking by Barnsley and watched a Dean Howell own goal prevent a perfect start.
Howell's mistake cancelled out Daniel Nardiello's earlier penalty, although Northampton's Chris Hackett also missed a spot-kick.
Flitcroft said: "I want to find out about my team, I want to find out about what the fans want and I want to find out what this project is about.
"I've done that. We got a point and we've got something to build off but over the next 48 hours, I'll have to find some solutions.
"I told the players after the game we've got some hard miles to get where I want to go and match my professionalism and dedication.
"Our second half performance was just a grind and a fight and a smash-up. I don't believe that's what League Two football is about.
"We don't keep the ball well enough. It's not been part of the everyday training and it's not part of any ideology and ethos at the club.
"That's completely opposite to where I'm at as a coach and a manager. We're quite a way off where we need to be but I'm sure we'll get there."