The three-time Grand Slam winner progressed to the Round of 16 after a straight-sets victory on Centre Court.
Martinez was forced to take a medical timeout during the opening set, but showed immense heart to battle through to the end of the contest.
Sinner insisted it was not easy to play on grass when your serve was held back by a shoulder issue.
“Obviously I am very happy but I think that we all saw that he was struggling with his shoulder,” Sinner told the BBC.
“He could not serve very well and, especially on this surface, when you don’t serve well it is not easy to play.
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“But huge respect for him to come out here and compete, it was not easy for him.
“But from my side, I tried to stay solid from the back of the court.
“We had some very good rallies.”
Sinner cruised through the opening game of the match before breaking his opponent to double his advantage and take control of the first set.
The Italian then held serve and followed that up by producing his second break of the match to extend his lead to 4-0.
The match was delayed between the fifth and sixth games of the opener after Martinez called for a medical timeout to deal with what appeared to be an injury to his right shoulder.
That sparked Martinez into life, and he held serve in the next game to make it 5-1, but Sinner seemed unfazed and wrapped up the opener with ease.
The two traded games at the start of the second set until Sinner produced another break in the fifth.
That made it 3-2, and he doubled his advantage shortly after as the match continued to slip through Martinez’s fingers.
As the second set progressed, Martinez had the chance to break back, but Sinner came out on top in a closely fought eighth game to make it 5-3.
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Sinner then produced another break to secure the second set.
It was more of the same from Sinner at the start of the third. He produced another break to storm into a 3-0 lead and within a whisker of the win.
Sinner’s second break of the set meant it was 4-0 shortly after and he held again to extend his advantage.
Martinez finally got on the board to keep the match alive, but Sinner held serve to wrap up the victory.
 
			 
			 
			