Published: 2019-11-03 03:34:18 BdST
Barca had returned to the top of the table by thrashing Real Valladolid 5-1 in mid-week for a seventh straight victory in all competitions and put themselves in a comfortable position when Lionel Messi converted a penalty in the 38th minute.
Their problems began when Luis Suarez was taken off injured a few moments later and they collapsed in the second half, with Levante scoring with all of their first three shots on target.
Jose Campana levelled in the 61st minute following a quick-fire counter-attack after winning the ball in Barca's half, then former Real Madrid striker Borja Mayoral put them ahead in the 63rd with a superb curling strike from outside the area.
It was Barca's third defeat of the campaign and they still lead the standings on 22 points after 11 games but Atletico Madrid and Real Madrid can both climb above the Catalans if they win their matches later on Saturday.
Levante, who have won three of their last four home fixtures against Ernesto Valverde's side, moved up to eighth in the table on 17 points.
"It was an even game but they took advantage of those seven minutes. It wasn't a great performance from us but the result is excessive," Barca midfielder Sergio Busquets told reporters.
"We didn't create much but in the second half we did ourselves a lot of harm with that spell when they scored three times.
"They committed a lot of players forward and got themselves into better positions than us. We're going to try and stay positive, we were on a great run which has now been broken but we're still top and we have a lot more games to come."
Barca coach Valverde made four changes to his team from the Valladolid game, bringing 120-million-euro signing Griezmann back into the line-up at the expense of teenager Ansu Fati while starting without Busquets, Jordi Alba and Arthur.
The manager, who has won the title with Barca for the last two seasons, was asked after the defeat if he was considering his position but emphatically ruled out stepping away.
"Our aim was to try and go for a second goal after taking the lead but we weren't able to create enough danger. We lacked organisation after the second half and had little control."
Griezmann struggled to explain Barca's collapse after the interval.
"When you concede three goals in a few minutes then it could be a problem of everything, attitude and our style of play. We have to do everything to stop this happening again," said the French forward.
"We didn't start the second half well but there's nothing we can do about it, we can only improve and learn. Anything can happen in a game but it's how you react, and we didn't react properly today."