"Thanks again for ALL the messages and kind words," he wrote on Twitter. "But yea I'm doin ok and in the market for a new car! Lol..Gotta try to find some humor."
The incident was described by a Rangers spokesperson as "disturbing and deplorable," though police do not believe it was a sectarian attack.
A witness saw a hooded figure plant the bomb and run off. A car then sped past the fire.
"The guy put something under the car," the witness told the Glasgow Daily Record, "then walked backwards crouching down, making a line of petrol for about five meters. He lit it with what looked like a lighter and the car went up."
Beasley ran to his window after he heard the car's screeching tires and saw his car on fire.