The Giallorossi's hopes of qualifying for the Champions League took a massive blow with a 4-2 loss to relegation strugglers Lecce, which had been 4-0 until the final minutes.
"The worst thing is the result, without doubt," said Luis Enrique. "We didn't get into the game and once we conceded the first goal, it was an uphill struggle.
"We do have limits, as we are unable to turn games around. I am disappointed, as are the players. I never talk about individuals when things go badly and I take full responsibility.
"We will try to work in order to improve our defending from set plays, but all teams struggle with these situations. We definitely have to do better away from home.
"Resign? I never considered resigning and I don't know where these rumours come from."