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After arriving at the tournament on the back of just one warm-up game all year, the Pumas pushed England all the way in losing their pool opener 13-9 last week then cut loose at Rugby Park, running in four tries in a blistering opening half-hour.
"The team is growing and that was one of the aims of the tournament, to grow match by match, and that gives us confidence for the big game against Scotland," Phelan told reporters, looking ahead to next Sunday's match that will probably decide the runners-up spot behind England.
"We played a very good first half, we started really well. We didn't play quite as we wanted in the second but it was important to get a lot of points, something we haven't achieved for a while, and we are continuing to grow."
After the Argentine pack did most of the work in the England game it was the turn of the backs to sparkle on Saturday as they ran hard, straight lines and moved the ball crisply in an impressive display against some albeit poor tackling.
Phelan said, however, that he had yet to even think about what approach he would take to next Sunday's clash, where the winners can expect a probable quarter-final meeting with hosts New Zealand.
"We are taking it game by game, we haven't even discussed a plan for the Scotland game yet," he said.
Captain Juan Martin Fernandez Lobbe said he was particularly pleased with the way the players followed the pre-game plan.
"We had no option but to win but I'm happy with the way we won," he said.
"There were long periods where we stuck to our game plan and we scored tries from that, which was good.
"After we got the fourth try maybe we lost a bit of structure but we talked about it at halftime and got back on track later on."
Romania coach Romeo Gontineac was desperately disappointed that his players failed to match the effort they showed in their opening game against Scotland, particularly in the first half when their tackling was feeble at times.
"I can't be happy with that, we just weren't in the game," said Gontineac, whose team led the Scots with six minutes to go last week before eventually losing 34-24.
"You can't play without being aggressive.
"There were some positives -- we scored a nice try and in the second half we defended well and aggressively -- but you cannot play rugby if you are not combative.
"Argentina played a wonderful game, they beat us in all areas. They were strong up front and very agile, but this was not the rugby we can play and what you saw against Scotland.
"There was some panic in the first half and we gave away a lot of points.
"We started badly against Scotland and very badly today. "That's a collective problem but it's something we can fix, that's up to us.
"We changed some players today because we wanted to play more rugby but it didn't really work out that way."