Alcaraz's preparations for his Wimbledon title defence suffered a set-back on Thursday with his 7-6(3), 6-3 loss to Draper in the last 16.
The 25-second shot clock, aimed at reducing the time taken between points, was previously started only when the chair umpire called the score but media reports said a rule tweak sees the countdown to a serve begin almost immediately after a point is concluded.
The reports said the new regulation was on trial for the last 10 days and players had been informed about it.
Alcaraz said he had no time to go through his regular routine during the match and that he had expressed his concerns to chair umpire Mohamed Lahyani.
"He told me that there is a new rule, this new thing, that the clock never stops. After the point is finished, the clock is putting on," he added.
"I think for the players it's something bad. I finish the point at the net and I had no time to ask for balls. I'm not saying to go to a towel and take my time. I feel like I can't ask for the balls.
"It's crazy. I have time just to ask for two balls and no bounces. I've never seen something like that in tennis.
"If you play a long point or finish at the net, you have time just to go for a towel or ask for your routine, ask for, in my case, four balls, I'm concentrating on the next point, just bouncing my bounces and serve as best as I can.
"Today I felt like I was in a rush all the time. I had no time to bounce and do my routine."
Reuters has contacted the ATP for comment.
The French Open champion was asked if he had spoken to the governing body.
"Not yet, but I will, for sure," said Alcaraz, who will now head to Wimbledon, which begins on July 1.
