The Red Devils endured a frustrating first half against the tournament debutants, who defended in numbers and got to half time without conceding.
"I'm delighted," Martinez told reporters. "It was exactly what we expected - there are no easy games at the World Cup.
"We started very well but then became frustrated as the first half wore on. But I was delighted in the way the team reacted and the commitment everyone showed to keep a clean sheet.
"In the second half we found our composure and the goal from Dries Mertens, a great goal, was so important for us.
"In a World Cup, you have to play for 90 minutes and we had to be prepared to work hard, show maturity and real togetherness."
Belgium return to action on Saturday against Tunisia at the Otkrytiye Arena.