With Boro leading 1-0 in the 69th minute of the encounter at the Riverside Stadium, referee Kevin Friend controversially awarded City a penalty when he felt Leroy Sane was fouled by Marten de Roon, sparking protests from the home side.
Sergio Aguero scored the resulting spot-kick before Callum Chambers restored Middlesbrough's lead, but Gabriel Jesus headed another equaliser in the 85th minute to leave Agnew's men six points from Premier League safety with three games left to play this season.
And a frustrated Agnew told reporters: "I was disappointed that we didn't see the game out. I thought the lads were terrific and deserved the three points.
"I didn't think it was a penalty. I thought the player went down very easily and from the video that I've seen the referee didn't have a clear view. I think that, when you give them, you've got to be 100 per cent certain."
He expressed sympathy for De Roon, saying: "He's a top professional and a very intelligent boy. He knows that when you're in the penalty area, he's not one for making contact.
"I was really pleased with the reaction from the players and the way they responded for the rest of the game."
Middlesbrough face Chelsea, Southampton and Liverpool in their final three games of the season, and Agnew said the performance against City would stand his players in good stead as they attempt to pull off an unlikely escape.
"We're six points behind with three games left, and we've got a good goal difference," Agnew said. "I think the players will take a lot of confidence going into Chelsea having played so well against Manchester City.
"The performance showed the determination and the fighting spirit of the squad. That was evident against one of the top teams in the country."