Steven Tyler Pays Tribute to 'Dear Friend' Hayden Panettiere

Steven Tyler and Hayden Panettiere stayed close after working together on "Nashville" ... and the rocker is shocked by the loss.

A photog got the Aerosmith frontman while he was out on Tuesday ... and at first it seemed like he didn't want to talk -- but then Hayden was mentioned.

Check out the video ... the two clearly formed a bond while working together on the popular ABC series -- where Tyler did a few guest appearances as himself.

As you know ... Hayden died on Sunday in a South Carolina apartment ... after she was found unresponsive.

TMZ broke the story ... Hayden and her boyfriend Brian were both inside an Airbnb in Greenville on Sunday afternoon when his brother Zach entered the residence and found Hayden in a chair in the living room, suffering cardiac arrest while Brian was asleep in a separate room.

First responders were dispatched to the residence and attempted life-saving measures ... but Hayden could not be revived and was pronounced dead a short time later.