The Italians come into the game on the back of a frustrating 26-23 defeat at home to the Scarlets but Phillips is confident his side will perform better against Eric Elwood's men.
He said: "There was the opportunity to win against the Scarlets. To beat them you have to win the physical battle in the forwards.
"We did that for the majority of the match, but there was something extra missing. But I am really happy with the scrum, with Lorenzo Romano playing very well, I'm pleased with the offensive and defensive structure.
"We probably just lacked a little calmness in the decisive moments, especially when we went into their 22 we didn't have the patience required to take advantage of the chances we created.
"We have grown from the squad that was here last year. In Galway I'm expecting another step forward to build the mentality away from home that we show every time we play at home.
"It would be a shame to have to stop this work which we only feel is half done."
Phillips has made just one change from the side which lost to the Scarlets with Italy winger Giovanbattista Venditti returning in place of Gilberto Pavan, with Sinoti Sinoti moving to centre.
Connacht, meanwhile, come into the game on the back of two straight wins over the Dragons and Ulster, and head coach Elwood has chosen to make just one change.
Denis Buckley comes into the front row in place of the injured Brett Wilkinson and Elwood admits he is desperate for a strong end to the RaboDirect PRO12 season.
He said: "We're looking for a strong performance and to finish the season on a high. We've had some excellent results in recent weeks and we hope to build on that and finish on an up.
"It'll be a big day for the likes of Ray [Ofisa] and Henry [Fa'afili] playing in front of the home crowd for the last time so it would be great to give them the send off they deserve and finish with a win."
At Sportsground, 5pm.
Referee: Ian Davies (WRU, 1st competition game)
Assistant Referees: SimonMcDowell, Stuart Gaffikin (both IRFU)
Citing Commissioner : TomMcCormack (IRFU)
