A point apiece means the gap between the relegation rivals remains eight points at the foot of League One.
But the game's main talking point was referee Geoff Eltringham's decision to send off U's striker Ibehre two minutes before half-time following a challenge on Pools' defender Neil Austin.
"The sending-off, I've looked at it again and we'll be appealing straight away," said Dunne.
"It was a fair challenge, no studs showed when he made it. The laces were going for the ball. Austin got straight up to his credit.
"It was harsh, maybe the referee's angle made it hard for him, but he had a difficult game. Jabo was harshly sent off."
Dunne was full of praise for his players' efforts with reduced numbers.
He added: "It was a fantastic defensive performance, we can take joy from it.
"As a team we defended exceptionally well. We had to change it around with the sending-off and we did a lot of tactical work at half-time and changed it during the game as well.
"They had a lot of possession and chances, but we were strong and stout. The defenders were out on their feet, we changed things around a bit and played 3-4-2 which was quite brave later on."