Ronaldo had set up Jese's 65th-minute opener at San Mames but was given his marching orders soon after.
Ibai had levelled proceedings for the hosts eight minutes after Jese's goal before Ronaldo was red-carded.
The star attacker was pushed by Carlos Gurpegui before retaliating by lifting his hands up to the defender's face.
Ander Iturraspe got involved and appeared to headbutt Ronaldo – receiving a yellow card – and the Portugal international looked to have responded by scratching him.
Gurpegui may have gone down theatrically in the first incident but referee Miguel Ayza appeared to be sending Ronaldo off for his altercation with Iturraspe.
"It's tough for me to say because I was not close to it but the pictures show that it was a bit exaggerated," Ancelotti said, likely refereeing to the Gurpegui incident.
Bilbao coach Ernesto Valverde said he had not seen the incident but felt the red card must have been there.
"I don't know, I didn't see it, but he's obviously done enough to be sent off," he said.
Ancelotti was content with his team's performance, with Bilbao needing a cracking 73rd-minute strike from Ibai to grab a point.
The Italian coach said failing to properly clear the set-piece which led to the goal was the only chance his team gave up.
"We played well. It was a high intensity match and we hardly let them have any chances," Ancelotti said.
"We did especially well in the second half. It could have been different because we scored first and dominated the match afterwards.
"Athletic Bilbao scored a fantastic equaliser but overall we are going away satisfied with how we played."
Ancelotti said only a 'great goal' had denied Real, who sit third and three points behind La Liga leaders Atletico Madrid.
"After Jese's goal we had control of the match and did not suffer. The team was well-balanced but Ibai's goal was a fantastic strike," he said.
"We did not make any mistakes, it was a great goal. We hardly let them have any chances – just one in the first half and none in the second half."
