The Foxes put in a below-par display, which allowed them to slip to defeat thanks to goals from Jonjo Shelvey and Ayoze Pérez.
Jamie Vardy hit a consolation for Leicester, but it was too little and Puel rued the 'good opportunity' his side had missed.
Poor first half
“I think today we didn’t play well enough in the first half and it was the same feeling as last week at Brighton,” Puel told media after the final whistle.
"We repeated this performance today and we have missed a good opportunity.
“It is not finished (the race for seventh) but we have to correct this and to start well in games," the Leicester boss added.
Puel continued: "It was too poor in the first half without the good tempo, the good quality and aggressiveness without the ball.
“We have to correct this aspect of our game. We have to perform from the start of the game, because after we have to keep react from going behind."
"We have to correct this,” Puel stated.
Worryingly for Leicester, former Sevilla midfielder Vicente Iborra picked up a hamstring injury during the first half, leaving Leicester's central midfield department depleted for the Foxes' trip to Burnley.
Young Development Squad midfielder Hamza Choudhury replaced him and put in a Man of the Match performance on his Premier League debut.
“Iborra has a hamstring injury and we have to see," Puel explained. "He will be examined and undergo tests tomorrow but we are unlucky at this end of the season with our midfielders.
"After the surgery for Matty James, the sending off which wasn’t deserved for Wilfred Ndidi, it is now Iborra."
"It is a good thing now to have a young player like (Hamza) Choudhury coming in through," the Foxes boss said.
"I think he is perhaps the only satisfaction from the game today because he came into the game with good quality, aggressiveness and tempo.
"He worked very hard and cut out a lot of dangerous balls for us because we pushed a lot in the second half," Puel added.
"It was a good performance from him.”
Leicester City travel to Turf Moor on Saturday as they look to close the gap to seventh-placed Burnley.