Dr Sarandev Bhambra was singled out by Zack Davies who was heard saying "white power" during the machete attack at the store in Mold, Flintshire, in January.
An ex-soldier rescued the victim.
Davies, 26, of Mold, was convicted of attempted murder at the town's crown court in June and on Friday was told he must serve at least 14 years in prison.
Judge Rhys Rowlands said Davies had developed "extreme racist views" and had been plotting to carry out a "murderous attack" in order to draw attention to himself.
He said it was a "planned and racially motivated attack", as Dr Bhambra watched proceedings during his first appearance at the court in Mold.
Speaking outside court, the victim said Davies was a "coward".
"He attacked me from behind and tried to behead me," Dr Bhambra said. "By the grace of God I remained conscious and was able to defend myself.
"It is abhorrent that he has claimed that he tried to kill me in Lee Rigby's honour."
During the trial, the court heard Dr Bhambra had been walking down an aisle in the store on 14 January when he felt a "huge blow" to the back of his head from the 30cm (12in) machete.
Shopper Leanne Jones said she heard the words "white power" and that Davies was acting "like a lunatic" as he hacked Dr Bhambra with the machete.
Another witness heard Davies say: "Come here, this is for Lee Rigby".
The attack left Dr Bhambra, a 25-year-old dentist from Leeds, with two deep cuts to his scalp and another to his back, which went down to the muscle.
An injury to his left hand caused major nerve, artery and tendon damage, leaving him in need of surgery for five hours.
If it was not for the "remarkably brave actions" of soldier Peter Fuller, who came to his defence, Dr Bhambra would have been "killed in front of many shoppers", Judge Rowlands said.
The trial heard items associated with white supremacy and Nazism were found at Davies's home, including banners, swastika badges and Combat 18 stickers.
He also said he was "absolutely fascinated" with Islamic State and described the British man known as Jihadi John as his inspiration.
Michael Adebolajo and Michael Adebowale were jailed for life in February 2014 for hacking Fusilier Rigby to death.
After the trial concluded, Dr Bhambra's brother, Dr Tarlochan Singh Bhambra, said his family had "no doubt" that, had the "racial disposition" of the case been reversed, it would have been reported as an "act of terror".
Det Ch Insp Alun Oldfield from North Wales Police said: "This was a horrific attack and we are pleased with the sentence given to Davies.
"North Wales Police would like to commend the character and determination of Dr Bhambra and we are delighted that he is making such a good recovery.
"We also applaud the actions of Mr Peter Fuller, who has since been nominated for a national bravery award."
A neo-Nazi has been jailed for life for attempting to behead a Tesco shopper in a racially-motivated revenge attack for the murder of Fusilier Lee Rigby.