Inter twice came from behind in the final 11 minutes to salvage a dramatic 2-2 draw at home to Napoli in Serie A.
Jose Callejon had given Napoli a 79th-minute lead before Fredy Guarin restored parity in Milan three minutes later.
Callejon was at it again in the final minute to restore Napoli's lead but Hernanes equalised in the 91st minute as under-fire coach Mazzarri avoided defeat against his former club.
Speaking in the absence of a fatigued Mazzarri, Ausilio told Sky Sport Italia the Italian boss had the support of the playing group amid a three-game winless streak.
"I think the team today showed today that we are all united [behind Mazzarri]," he said.
"[Why didn't Mazzarri do the interview?] The coach was very tired and very nervous.
"He will speak ahead of the next game on Wednesday. He has apologized but that is the way it is today."
Prior to kick-off at San Siro, speculation was rife in the media that Mazzarri's time at Inter could be over if they lost a third consecutive league match.
"In Italy we are accustomed to this type of situation," Ausilio added.
"But we have a club and a president that are solid and the team showed with this performance whose side they are on. We are united and can continue from here."
