Belgium dispatched their visitors with minimal fuss in Nicosia as Eden Hazard – making his 100th international appearance – gave them an early lead.
Michy Batshuayi made it 2-0 eight minutes later and that proved to be as good as it got, as Belgium subsequently took the sting out of proceedings and eased to the finish.
Although some might have expected Belgium to go on and win by a greater margin after going two up just 18 minutes in, Martinez was content with a relatively narrow victory.
"This type of match is difficult if you don't start well," Martinez told VTM. "Certainly, because the pitch was very dry.
"Fortunately, we started well, with a lot of sharpness, and two early goals as well. After the break we had control and we played very mature.
"The six points out of six is the perfect reward for our hard work, but nothing has been decided yet.
"Now we have to focus on the next two matches against Kazakhstan and Russia [in June]."
Batshuayi was also keen to highlight the importance of early goals, particularly from a personal point of view.
"Goals are like vitamins to me. I live from them," he added. "It was difficult, for me and for many other players.
"The circumstances were not ideal, on the move on a difficult pitch, but we have been efficient in the first half. That has paid off with two quick goals.
"We have got six points out of six. We are three points ahead of our rivals, and we are Belgium: we don't look behind us, we only look ahead."
The Red Devils claimed a 3-1 victory over Russia in their opening qualifying game, with Youri Tielemans netting the opener and Hazard scoring twice.
That win coupled with Sunday's 2-0 result has helped Martinez's team pull some momentum back in their favour after suffering a disappointing 5-2 defeat to Switzerland to end their Nations League campaign in November.