Davis has been in top form all season and put 41 points on the board against the Heat.
But with little support, the power forward was unable to drive his team to victory single-handedly.
Rumours have been rife over recent weeks that Los Angeles Lakers and Boston Celtics are interested in signing Davis.
And the 25-year-old only added fuel to the fire by coming out and highlighting his team’s issues following their most recent defeat which leaves them 11th in the Western Conference.
“It’s been an issue,” Davis said.
“Not every game, but I think we come out too lackadaisical at times.
“It’s normally against a team that’s under .500 or stuff like that.
“We’ve got to come out and play these games the same way.
“[In the last game] we played a different way because we lost to Washington, so we came out with a little more urgency because we lost to them before.
“We’ve just got to come out and play the same way we’re supposed to at all times.
“It’s tough playing down every game, playing from, 30 tonight, and then use all the energy we’ve got to catch back up.”
Davis can buy himself out of his Pelicans contract at the end of the season.
And according to NBA reporter Chris Sheridan, Davis is considering a move to link up with LeBron James in California.
“Contrary to what has become gospel in the NBA rumour mill — Anthony Davis is a lock to end up with the Los Angeles Lakers next season,” he wrote.
“The situation with one of the league’s top three players remains fluid. For now.
“But most importantly as it pertains to the Eastern Conference, the Boston Celtics are very much in play as the ultimate long-term landing zone for the best player on the New Orleans Pelicans.”