Aironi led the encounter for the majority of the second half and looked odds on to win their third game of the season as three Naas Olivier penalties gave them a six-point lead over the visitors with minutes remaining.
But the Dragons are looking to bring European rugby to Rodney Parade next season and seized their chance in this match after the sin binning of hooker Fabio Ongaro two minutes from time.
Up against a depleted Aironi pack the Dragons eight scrummaged themselves to a penalty try and the subsequent conversion by replacement fly-half Lewis Robling won them the gameand it is the set piece that Phillips believes was their key failing.
"In the last play of the game our discipline went," admitted Phillips.
"We conceded two penalties and then a yellow card arrived.
"In general play we lacked calmness when we arrived in the opposition half.
"We played well but we lost 4 out of 22 lineouts and above all at the end we should have played tighter and looked for the penalty that would have closed the game.
"It's still a last-second loss but I have seen good things.
"In Swansea (where Aironi lost 23-7) we created a lot, and here we did even better."
Guinness PRO12 Aironi News
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