(I'm a Muslim). I mean... Strictly speaking as far as i am aware the mat/rug is not sacred itself. It is just a place to put your head +knees comfortably.

In fact the Prophet Muhammad SAW did not use a prayer mat and instead he placed his head on the soil (ground/earth).

Also note; Shias place their head on a stone/rock to mimic this practice: https://en.m.wikipedia.org/wiki/Turbah

Yes, the prayer rug is not sacred, per se, but it can be embued with a measure of sacredness by our practices upon it.

Please know that Zikr (remembering/repeating one of the many Names of God) is the highest form of worship. (Zikr is commanded three times in the Quran-i-Kerim.)

Al-lah, Yah-weh, Di-os, De-us, Brah-man, ...

Many Names in our various languages for the one Creator, one human race, one religion of God: compassionate service to all mankind that comes in many forms across our planet's cultures and epochs.

Always love. Teach to always love. Never hate. Teach to never hate.