Burns' half-back partner Michael Dobson will also have scans on a foot injury on Monday to reveal the extent of his injury.
Sandercock said: "It's a tragedy for Travis, he's broken his arm so that's him done for the season. Travis is one of our best players and it's going to be real tough for us now.
"Michael (Dobson) will go for scans tomorrow on his injury. He should have come off but he is a tough character and stayed on and led us round the park well in the second half even on one leg."
Widnes led 24-0 early in the second half but Rovers staged a brave second-half rally to cut the deficit to just six points at one stage.
Sandercock added: "Widnes were too good and real enthusiastic in that first half.
"To their credit they deserved to win, but I was pleased with the way we battled back and gave ourselves a chance playing some of the footy we can play.
"It's disappointing and we knew it was going to be a tough game against a Widnes team playing really well and Gareth Hock and Kevin Brown are class players and today showed why."
Widnes coach Denis Betts felt the opening period, when his side built a 18-0 lead, was the best rugby they had produced all season.
Betts said: "I think the first 40 minutes were the best we have played all year. Even though we were good at Warrington and worked hard, our intent and purpose and sting in attack and defence was relevant about how we went about our business.
"There were some real good shots and intent on how we wanted to defend and to keep a good attacking side like Hull KR to nil at half time showed a very tough performance.
"By the time of the Hull KR fightback I thought we should have been 50 points up, we had a few more opportunities and the referee seemed to find every single one of our forward passes
"But we just got a bit edgy by not finishing off our chances and it could have been at least 40 to 50 points before they were even on the scoreboard.
"To go toe to toe with a side in the eight with the likes of Michael Dobson and Craig Hall in the opposition it was a big effort."