Caleb Okoli’s first-half header was enough to earn the former Southampton and Rangers manager victory as he looks to turn Leicester’s fortunes around following relegation to League One.
“There were loads of good moments and loads to improve on,” said Martin. “I’ve told our players to enjoy but they are not happy.
“We didn’t create enough in the final third and there is loads to work on, there is so much room for improvement with this side.
“I really enjoyed my first game. People have been brilliant and I hope our fans are feeling positive, we certainly are.”
Leicester gave debuts to Liam Cullen, Tommy Watson and Wes Burns and Martin added: “We have had to be patient but we will add to this squad. We are making this squad better.”
Chris Hogg was also in charge of Northampton for the first time and was watched by close friend and former Norwich and Bristol City manager Liam Manning.
Hogg said: “Liam was here as a friend and spectator and I’m sure he will give me a good debrief when I call him on the way home.
“I hate losing but I’m super proud of the boys. Leicester have a top manager with a good style of play.
“The travelling support was special, they came in numbers and were terrific. They gave us energy. We want to build that connection.”