Wilson's men now face current world champions South Africa on Tuesday in Vannes for a place in the final.
"The boys showed a huge amount of character to come through against Argentina in the end," said the Wales head coach.
"We played some good rugby in the first half but our performance level dropped off slightly in the second half and Argentina came back hard.
"It was brutal, as we expected, and we have a lot of bumps and bruises to nurse before Tuesday's game but we defended well and we are now in a good position to kick on.
"South Africa are world champions, they are a very good side.
"But we are confident that if everyone can recover in time to be available for Tuesday's semi, we can compete with the best in the world.
"We showed that last year by beating New Zealand and we have showed already in this tournament that we are able to mix up our game plan depending on the opposition.
"Argentina beat South Africa twice before coming to France, so although we respect all our opponents, we have nothing to fear."