Martin O'Neill, meanwhile, insisted his Republic of Ireland team can defeat Italy next week and remain in Euro 2016 after defeat in Bordeaux left them needing just three points to avoid another group stage exit.
"We were under pressure before today", Belgium's Kevin De Bruyne, the game's outstanding player, said.
"Naturally it would have changed the course of the game if we had been given a penalty and scored, but we have been beaten by the better team".
O'Neill told reporters on Saturday: "We must go and try to win - that can be our only thought". "We win and lose together".
Wilmots said: "Well, after four years of success, when we get criticism it's like those last four years disappear".
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Belgium now has three points from its two games at Euro 2016, while Ireland has one.
Ireland struggled to retain possession and were repeatedly hit on the counter-attack and they will have to be considerably better against the Italians if they are to fix the damage.
With Conte's charges securing the top of Group E with a game to spare, their odds of making it all the way may not be as good as we'd assume.
"I can't really say what he was thinking because the pictures speak for themselves".
After being frustrated by the Irish in the first half, Belgium broke through when Lukaku struck three minutes after the restart, atoning for his profligacy in front of goal in Monday's 2-0 loss to Italy.
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Ireland meets Italy, which has now won the group.
Lukaku opened and closed the scoring, bookending Axel Witsel's picture-perfect header, as their victory consigned Ireland to the bottom of Group E.
Italy could rest stars Gianluigi Buffon, Leonardo Bonucci, Eder, Giorgio Chiellini and Daniel De Rossi as they are all one booking away from missing the Last 16. "We spoke about this privately". "We have to be positive, that is the most important thing".
O'Neill had promised to reserve judgment on how many Belgium players would get into the Ireland team until after this game and that turned out to be a wise decision on the manager's part.
"We were hoping to rectify that at half-time, and the disappointment came from the fact that they have broken on us for their first goal when in actual fact the ball was bouncing around their penalty area in the first place from the free-kick that we had". But, as it tends to be the case with most golden generations, they have yet to live up them. Then you start to chase the game and you get stretched.
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Appeals for a penalty before the first goal, when Shane Long was kicked in the head by Toby Alderweireld, were rejected and O'Neill feels it was a game changer. This time round, they could be right.