Dries Mertens and Nacer Chadli scored in Belgium's 2-0 Group H victory away from home on Friday.
In-form Napoli star Mertens opened the scoring before Estonia's Artjom Dmitrijev was harshly sent off on the stroke of half-time.
Chadli sealed Belgium's win as Martinez's unbeaten side opened a four-point advantage over Greece.
There was a sense of relief post-match with players keen to enjoy some time away during the off-season.
"It was really a tough match," Martinez told RTBF .
"It was a difficult time for us to stay in the midst of the players' vacation, but we were very concentrated, we were patient, we were able to keep this discipline.
"It was a bit of a tricky game, we did well, but that second goal is important. It's true that it happened quite late, but if it had come earlier, it would have changed things but we created a lot of opportunities.
"The most important was to manage the game well and keep a clean sheet."
Mertens said: "It was very difficult, they played very well together, everyone was a bit tired.
"It was very difficult to play on a field like that. But in the end you get the three points and everyone thinks you win 7 or 8 against teams like that, but that's not the case."
Belgium captain Vincent Kompany added: "It was a good performance. We had a difficult terrain and an organized team against us. Even the small teams know how to protect their goal now."