World Cup-winner Tindall blasted the RFU for handing Borthwick a "hand grenade" for this global tournament in France, after appointing the former England captain as head coach in December.
England enter the World Cup at their lowest-ever world ranking of eighth and off the back of three defeats in four warm-up matches.
Borthwick and his coaches continue to maintain there are no massive concerns and that there is still the chance to turn recent form on its head in Saturday's crucial Pool D opener against Argentina in Marseille.
The Pumas are now ranked above England, however, and boast a hungry, physical pack, astute playmakers and razor-sharp finishers out wide.
England are in disarray in the run-up to their World Cup opener at Stade Velodrome, but 2003 tournament winner Tindall believes Borthwick must not carry the can if the Red Rose wilts in France.
"I would say you can't sack him," Tindall told the Lawrence Dallaglio Evening Standard Rugby Podcast. "You can't give him the hand grenade you've given him, then sack him straight off the bat. Even Eddie Jones has come out to defend him and blame the RFU."
Iconic England World Cup-winner Dallaglio will once again front the Evening Standard's Rugby Podcast throughout the global tournament in France, which gets under way on Friday with hosts France taking on the All Blacks.
Dallaglio will welcome a host of top rugby guests and star names, along with co-presenter Sarra Elgan. The first offering, with special guest Tindall, is out today on all usual podcast platforms, with new episodes weekly until the end of October.
England sacked Jones after a wretched autumn series, with Borthwick installed along with a new coaching team at multi-million pound expense to the RFU.
The former Leicester boss was given only nine matches to whip England into World Cup shape and his teams have lost six of those outings across the Six Nations and August Tests.
Now comes the crunch, though, with the fizzing Pumas ready to unleash their typically emotional and brutal brand of rugby on a chaotic England.
Talismanic former England No8 Dallaglio has been as critical of Borthwick's operation as anyone, and urged England to dispense with the siege mentality that has been built up among the squad.
"The enormity of Saturday's game can't be underestimated for England," Dallaglio said on the first show on Tuesday. "If they win, all of the disruption goes away immediately. If you beat Argentina, suddenly the England squad are feeling happy with life. Lose that game, and it's a tricky time ahead.
"They appear to have a siege mentality at the moment, which is slightly worrying. It can work, but it's not the way to operate a world-class team."