Gonzalo Higuain's early goal was enough to decide the contest after which Wilmots said he was proud of his team but derided Argentina's approach.
Wilmots also claimed Lionel Messi was given an easy ride by referee Nicola Rizzoli of Italy.
He said: "We were not impressed by the Argentines, they were just an ordinary team. They can disturb the rhythm, they take 30 seconds to take a throw-in and the referee doesn't do anything.
"They had the goal, and Messi was one-on-one with Thibaut Courtois at the end, but how many shots did they have? If I played that way I would have been destroyed by the Belgian press.
"They didn't give us any space, this was a World Cup quarter-final and their extra experience probably counted for something."
Wilmots claimed the referee had favoured Argentina and in particular Messi. He added: "Every time something happens with Messi, the referee gives him a free-kick. I notice he made three fouls and there was no yellow card, we made one foul and got a yellow card."
Higuain's goal came when Vincent Kompany strayed from his position and the Napoli striker scored with a first-time shot.
Wilmots said: "We make a small, small mistake, Vincent came out of position and they scored. I'm very proud of the boys. I have told them 'you guys are the youngest of all the last-eight teams'. There was a great deal of emotion, some of my staff were crying in the dressing room because there is so much passion."
For all the post-match rhetoric, however, Belgium can have few complaints at the manner of their low-key exit. Higuain's excellent early strike provided the foundation for Argentina to make it to the last four for the first time since Diego Maradona's day in 1990 when they were beaten finalists.
The Real Madrid striker for once outshone Messi, but Maradona's spiritual heir also provided a constant threat that kept Belgium on the back foot.
Messi started off playing deep, seeing plenty of the ball and creating some good positions for his team-mates.
One such move put Ezequiel Lavezzi clear on the right and only Kompany's alert intervention prevented a goal.
It took less than eight minutes, however, for Argentina to take a huge step towards the semi-final and it was Messi, twisting and turning in midfield, who was the architect.
His incisive pass to Angel di Maria was diverted to Higuain, taking a nick off a defender which caused the ball to bounce up for the Napoli striker to swivel and thump a first-time shot low into the corner from 25 yards out.
Belgium rarely threatened in the first period, their best chance falling to Kevin De Bruyne, whose diving header bounced wide. The second half was strangely muted given what was at stake, with Argentina happy to keep things tight and Belgium failing to make much impression.
Marouane Fellaini, who had spent most of the match being bypassed by Messi, cut an anonymous figure and Eden Hazard was equally disappointing, his main contribution being booked for going in high on Lucas Biglia - on another day it could have been red - and he was soon replaced by Nacer Chadli. In the closing minutes Wilmots went for broke by pushing his tallest players, Fellaini and Daniel van Buyten, up front as extra strikers as Belgium threw the kitchen sink at Argentina. But the South Americans held out against the aerial bombardment, with substitute Romelu Lukaku and Axel Witsel coming closest.
Argentina coach Alejandro Sabella said his players deserved to reach the semi-finals for the first time in 24 years.
He said: "They will go down in history as one of the best four teams in the world and we will see if they can go one step more."
Sabella also praised Messi's contribution in a midfield role. He added: "Every move he makes endangers our opponents.
"The fact that a player like Messi almost never loses the ball is water in the desert, he gives us that water in the desert. Today when the terrain was dry he gave us that breath of fresh air every time he had the ball."