Italy's No. 1 Sinner produced a devastating display to outclass a helpless De Minaur after Matteo Arnaldi outlasted Alexei Popyrin in the first singles clash.
The two players have conveyed their unavailability for the World Group I play-off tie to be played in February but have not specified the reason behind their decision.
The AITA said the decision was taken after careful consideration and evaluation of Rajpal's successful tenure.
PTF president Salim Saifullah Khan said it will host India on grass court.
The 43-year-old Bopanna, coming out to play his 33rd and final tie, and Bhambri raced to a 6-2, 6-1 win over Elliot Benchetrit and Younes Lalami Laaroussi.
Sasikumar Mukund conceded the opening singles when the score was 7-6 (4) 5-7 1-4.
Digvijay Pratap Singh is the new face in the six-member team.
But the Karnataka player won't be able to play his farewell match in his home state, as desired by him, since the All India Tennis Association has already awarded the match to Uttar Pradesh.
India lost the tie 2-3 on Saturday with Holger Rune starring for Denmark.
Felix Auger-Aliassime beat Alex de Minaur 6-3, 6-4 to give them an unassailable 2-0 lead over Australia in the final.