And Phillips, whose team also beat Treviso at the Stadio Zaffanella just before Christmas, couldn't hide his delight at a second straight win.
He said: "What an attitude. The major satisfaction is that even in the last five minutes we didn't let them through.
"It would have meant a losing bonus point for them but instead we didn't allow them anything. I'm delighted with that.
"You could see there was the right spirit, and we had the confidence need to overcome the challenge of Connacht."
The win is especially pleasing with Aironi still missing try-scoring No.8 Nick Williams to injury but Phillips believes back rowers Simone Favaro and Nicola Cattina have performed admirably in his absence.
He added: "Of course the loss of Williams is something we have felt, but Favaro and Cattina are two examples to everyone for all the work they put in.
"They have grown a lot. As for the Six Nations? Yes, Simone definitely deserves to be there but it's not up to me.
"With the game against Connacht the initial cycle ended. In the next contests we might see a few changes."
Guinness PRO12 Aironi News
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