Madrid, who beat Levante 8-0 in the Copa del Rey last season, had their German midfielder Sami Khedira sent off in the 41st minute and Levante took advantage thanks to Arouna Kone's second-half strike.
Jose Mourinho, stung by the shock defeat, accused the winners of acting and said his own players are not comfortable with the "dirty side" of football.
"I don't want to take anything away from Levante's merit," the Portuguese coach said. "As always, here at their home they let them do as they want and they do it very well.
"I only have to congratulate them for being clever because they know how to provoke, they know how to fake it, they know how to gain time, they know how not to give the ball, they know all this which is also football. And here I can agree that our players are not at ease in this environment."
The result leaves Real three points behind joint leaders Valencia and Real Betis and one behind arch rivals Barcelona, who recorded an 8-0 win of their after thumping Osasuna.
Mourinho went on to blame the referee and the sent-off Khedira for their defeat, saying that in balance, one-sided decisions from the referee and not coping with Levante's tactics proved their downfall.
"As I was saying, the referee also has blame because a penalty and an expulsion is a lot, in a balanced game it is a lot too, and the blame is ours, mine and also all the players who were on the field too."
Elsewhere, promoted Betis made it three wins from three after edging a five-goal thriller against Athletic Bilbao at San Mames in a match that saw both teams end with a man down.
Betis stormed into an early 2-0 lead thanks to efforts from Benat Etxebarria and Nacho and, although Athletic pulled a goal back through Oscar De Marcos, Salva Sevilla's penalty on the stoke of half-time restored the away side's two-goal advantage.
Betis then saw defender Mario sent off in the 75th minute before David Lopez's 87th-minute penalty reduced the deficit to 3-2 and set up a grandstand finish.
However, the hosts could not force an equaliser and they too were reduced to 10 men in stoppage time when Fernando Amorebieta was dismissed.
Radamel Falcao enjoyed a fine day for Atletico Madrid as he struck hat-trick in a 4-0 win over Racing Santander at the Vicente Calderon — the Rojiblancos' first victory of the season.
The Colombia striker, a club-record signing at an initial €40 million (Dh200.8m) from Porto over the summer, struck in the 23rd, 36th (penalty) and 55th minutes before another new signing, Adrian Lopez, netted the fourth goal with 12 minutes remaining.
Luis Garcia returned to haunt his former club after netting twice — including a winner deep into stoppage-time — to give new side Real Zaragoza a victory over 10-man Espanyol.
Garcia, who left the Barcelona club this summer after six years, opened the scoring on the half-hour mark but Espanyol improved greatly after the break and were deservedly level when Javi Lopez's cross evaded everyone on its way into the net 19 minutes from time.
Garcia had appeared to have passed up the opportunity to win the game when his 86th-minute penalty was saved by Cristian Alvarez in an incident that saw Lopez dismissed for Espanyol.
However, in the final minute of injury-time, a Pablo Barrera cross fell kindly to Garcia at the back post and he fired high beyond Alvarez from five yards.
In the day's other Primera Liga game, an early effort from Miguel Perez Cuesta earned promoted Rayo Vallecano a 1-0 away win against neighbours Getafe in an ill-tempered clash.