Madrid fans jeered the team and Lopetegui, the former Spain manager who arrived to replace Zinedine Zidane after being fired two days before the World Cup.
While speaking to Omnisport, the 35-year-old Ghanaian hoped that Real Madrid do well under Lopetegui but if they don't then he will pay with his job as Real Madrid cannot afford poor form for too long, "Real Madrid are one the biggest clubs, so you can imagine the pressure, We all hope he will do well".
"Right now that is the last thing that I'm thinking about", said Lopetegui when asked if he was anxious about losing his job. "We have to sit down and think hard about what we are doing wrong and change our path". The ball is just not going in.
The Liga match between Real Madrid and Levante will be broadcast live on beIN Sports. "We must keep trying so that this feeling of playing well is translated into goals for us".More news: Paul George: 'I would have been in a Lakers uniform'
Jose Luis Morales struck after just seven minutes after a defensive slip from Raphael Varane and Roger Marti doubled their lead from the penalty spot soon after (13) when the France global was punished for handball.
Levante entered the game with the league's third-worst defence after conceding 14 goals in eight matches.
Lopetegui started with Mariano Diaz and Lucas Vazquez in the attack, with Bale and Benzema entering the match in the second half but not being able to help much.
VAR also ruled out goals scored by Real's Marco Asensio and Mariano.More news: Banksy implies shredding of $1.4M painting was incomplete
Madrid finished with 70 per cent possession and more than 30 attempts.
Real's last goal in any competition came in a 1-0 win against Espanyol on Sept 22 and they have failed to score in their following games with Sevilla, Atletico Madrid, CSKA Moscow and Alaves.
"I am just thinking about lifting them for the important Champions League game on Tuesday [against Viktoria Plzen] where we can turn this dynamic around".More news: Industrious Girl Scout Makes Bank Selling Cookies Outside Of Canadian Cannabis Dispensary