The Red Devils dominated for large spells but it took them until extra time to make the breakthrough as they went on to claim a 2-1 victory.
As well as praising his team for their display, Wilmots was delighted with the impact made by Romelu Lukaku, who set up Kevin de Bruyne for the opening goal, before scoring the decisive second soon after.
"We had a lot of opportunities, and we dominated the game, and in the end it was well deserved even if it was scary with the US goal," BBC Sport quotes him as saying.
"Lukaku had been much criticised, and I told him, 'do not worry - the second round might be your day', and that's what happened.
"Tom Howard had a fantastic match but we need to forget about this match and focus on Argentina. There shouldn't be any more worries from the media about us not playing football."
Belgium face Argentina in the quarter-finals of the tournament on Saturday.