The defender saved the Rossoneri from defeat in stoppage-time against Bologna on Wednesday, which he admitted was a "strange" game
The Rossoneri were 3-1 down on Wednesday but Robinho pulled a goal back with a minute left on the clock before Abate equalised in stoppage-time to make it 3-3, and the Italy international insists that the squad have the quality and spirit to do better.
"Milan have an enormous heart," the 26-year-old told reporters after the match. "We follow the coach and we’re playing good football right now.
"We fight in every game and we never give up. Unfortunately, nights like this are going against us at the moment.
"We have a lot of quality in our squad and now we have to show it."
Massimiliano Allegri's men dropped down to 12th in Serie A with only one win in the five games so far.
Abate, who branded the Bologna draw "strange", believes that Milan need to become more defensively sound if they are to rocket up the table.
"It was a very strange game," he added. "We played a good first half, but the first time we took our eye off the ball we conceded.
"If we had finished the first half two or three goals up then there would have been nothing strange about it.
"We’re playing well but evidently it’s not enough. We have to be more solid. We push forward all the time and it’s normal that we leave some space at the back."
Milan's next match is at home to Sampdoria on Saturday, though they will be without suspended striker Mario Balotelli for the second game running.