Engzell though defended Nadal and insisted he was taking a “reasonable” amount of time between points despite Norrie being left unhappy.
But the ruthless 13-time French Open champion still won 6-3 6-3 6-3 to reach the last 16 in Paris for a record 16th time – and then hit back at his fellow left-hander.
“Between games I think I need to take the towel, and I think I deserve to take the towel between games,” said the 20-time Grand Slam winner.
“Sometimes I think he was trying to speed up the situation, to put on some pressure. He’s free to do it. I don’t think I did anything bad.
“I didn’t complain at all when he was throwing his ball bad for 20 times. I didn’t know when he was going to serve.
“I didn’t complain at all during the whole match, so I don’t think he has to complain about the other stuff, no?
“The umpire just told me that I need to be quicker because he was ready. Okay, if he wants to put that pressure, I just accept it.
“I tried to be a little bit quicker. He was just playing his cards.”
In his post-match press conference, Norrie was less combative than on Court Suzanne-Lenglen.
“I was just playing at my normal speed, and I think he takes obviously a little bit longer, especially on his service games when he was serving,” said the best Brit in Paris.
“He does a good job of managing the time of when I’m serving. She did say something to him.
“I was having to wait until five, six or seven seconds left for him when I was the one serving when the rule is that you have to play to the service speed.
“I think it was all within the rules and completely reasonable – it didn’t put me off.”
Norrie, who reached two clay-court finals this season, preferred to look at the positives with Wimbledon only three weeks away.
“It was a wonderful experience playing against him, and I thought I played great,” he said. “I just don’t think I took enough risks.
“Let’s move on to the grass and get ready for some more tennis.”
Nadal, who has now won 32 consecutive matches at Roland Garros, will face next face Italian Jannik Sinner.
It was meanwhile a doubly bad day for Jamie Murray as the Scot went out in the third round of the men’s doubles with Bruno Soares – and then lost in the first round of the mixed with Bethanie Mattek-Sands.