Atletico Madrid spurned the chance to move level on points with Real Madrid on Thursday after conceding from two penalties, the second in the 89th minute, to draw 2-2 away at Levante.

Atletico led twice at the City of Valencia Stadium as Antoine Griezmann opened the scoring before Matheus Cunha’s first goal for the club looked to have sealed victory.

But each time Levante, who sit second bottom, hit back from the spot after a Luis Suarez foul and then a late handball by Renan Lodi allowed Enis Bardhi to convert from 12 yards.

“The reality is that we have to improve and quickly,” said Atletico coach Diego Simeone, who was also sent off towards the end of the contest after being given a second yellow card for dissent.

Atletico edge up to fifth, five points off early leaders Real Sociedad, who earlier returned to the top of the table after they won 2-0 away at Celta Vigo.

Goals from Alexander Isak and Aritz Elustondo in the second half were enough for La Real, who have not lost since going down 4-2 to Barcelona on the opening day of the season.

Simeone had said before the game he was “worried but busy” trying to fix his team’s unexpected fragility in defence, with this game making it seven goals conceded in the last three games.

Atletico have won only one of their last four league matches, against Barcelona, after a surprise defeat by Alaves and draws with Real Sociedad and now Levante.

Luis Suarez, Griezmann and Joao Felix started together again in a front three and it is possible that combining the trio’s talents in attack is coming at a cost to the solidity of the team.

Atletico face Liverpool at Anfield on Wednesday in what is a crunch game in Champions League Group B and they are likely to be punished again if they fail to tighten up against Mohamed Salah.

Griezmann’s opener came in the 12th minute as his corner was deflected back to him on the left of the penalty area. Griezmann hung up a cross to the opposite post and Felipe’s floating header across again found the Frenchman, who nodded in.

Levante equalised shortly before half-time when Suarez clambered over Ruben Vezo and Barhdi made no mistake.

Cunha, who joined in the summer from Hertha Berlin, might have thought he had scored the winner 14 minutes from the end when he was brilliantly slid through by Rodrigo de Paul and finished.

But Levante came again, Jose Luis Morales’ cross diverted onto the hand of Lodi at point-blank range, causing referee Pablo Gonzalez to consult the replay and award the penalty. Bardhi found the corner.