Monakana, signed on loan from Preston this week, scored one goal and made the other as Colchester came back from 1-0 down to take a 2-1 half-time lead.
But Bermuda international striker Nahki Wells scored his second goal of the match - his ninth of the season - to earn Bradford a point.
"We were resilient, we dealt with the long ball most of the time, we take a lot of positives out of the game and we can be pleased with our work," said Dunne, who was youth team manager when Bradford boss Phil Parkinson led Colchester to promotion to the Championship in 2006.
"We brought in Jeffrey Monakana to score goals and he did that for us although he is not yet fully fit.
"We have looked at Bradford' previous games and we thought we could create chances.
"We played well on the counter-attack and caused Bradford a few problems.
"Bradford started well and scored from our mistake, but we then took control of the game and we had the confidence to score two goals.
"We dealt with the crosses and a lot of corners in the second half and I am really proud of my players and pleased we didn't fold.
"Once or twice we looked threatening on the break and Gavin Massey hit the post."
Colchester ended the game with 10 men when 19-year-old defender Daniel Pappoe was sent off for bringing down Bradford substitute Mark Yeates in the first minute of stoppage time - only four minutes after coming on to the field.
Dunne said: "It looked as if he had won the ball, but it is how he won it. It was a challenge after the whistle had gone for a throw-in for us. There was no need to make the tackle, but he will learn."
Wells put Bradford in front after 14 minutes, the ball falling into his path from an attempted clearance by David Wright and he spun past Tom Eastman to slot the ball into the net.
But the lively visitors crowned a strong spell of pressure with two goals in four minutes. Monakana equalised after 28 minutes with an angled shot into the far corner after taking a pass from Craig Eastmond - the first time Bradford had conceded a goal at home this season.
Colchester went ahead after 32 minutes when Monakana's through pass split the Bradford defence and Jabo Ibehre fired past the advancing Jon McLaughlin.
Wells equalised with his second goal of the match in the 52nd minute when his looping back header from left-back James Meredith's cross deceived goalkeeper Sam Walker as the ball floated in the far corner.
Both sides went close in an exciting finale with Massey hitting the post and Walker turning a goalbound shot from Wells over the crossbar.
- Sports & Recreation
- Jeffrey Monakana
- Nahki Wells