Michael Jacobs twice gave the home side the lead, but Shrewsbury hit back quickly on both occasions.
After David Davies and James Collins had twice restored parity, Jon Taylor rifled home an 18-yard half-volley to break Cobblers hearts with three minutes to play.
"I've only been here for 24 hours so apart from seeing a couple of videos this was my first chance to see what we are good at and not so good at, and it was pretty much what I saw on the videos," said Johnson, who was confirmed as Ian Sampson's replacement on Friday.
"I can understand why the fans sometimes get frustrated with the team because we were decent for an hour of the game but then tired and looked fragile at the back.
"Shrewsbury finished the game the stronger team but we need to do that when we are playing at home. We kept giving the ball away when the players began to tire and that's something we need to work on at the training ground, mentally and physically."
Source: PA
Source: PA