The 33-year-old fly-half's enforced substitution - after taking several hefty tackles early on - dealt a huge blow to the defending champions hopes of bouncing back following their 32-20 defeat by England last Saturday in Dublin.
"He's sore, very sore", Townsend said of the full-back. "That was an excellent performance against Italy".
The teams will meet in their opening World Cup Pool A game in Yokohama on September 22, with the victor in that fixture likely to head the group and avoid a possible quarter-final with defending champions New Zealand. "Big, heavy forwards. But we've played against Montpellier and Toulon this year, so we know what it's like".
"Johnny Sexton got a bit of treatment out there and he got a stamp on the head but he is feeling better and we expect him to be back in the next couple of weeks", Schmidt said.
"We'd ideally like to play better and with more fluidity, and probably get on the front foot more", said Best.
'He is very sore, his shoulder is not right, we'll see. We'll look at ourselves and give credit to Ireland.
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Joe Schmidt has made five changes to the team that suffered defeat to England last weekend.
Lock Quinn Roux is promoted from the bench with Devin Toner (ankle) also ruled out and flanker Sean O'Brien is preferred to Josh van der Flier.
"Last week doesn't change the mentality too much", Schmidt insisted.
"But if we hadn't won this game, we were definitely out of it".
"So we thought there might be an opportunity and no better man to get it in his hands than Jacob".
After that, a handsome move that saw the ball change hands between Irish players in the middle saw Jacob Stockdale surge through and leave the Scotland forwards in his wake as he ran beneath the posts.
Scotland - 15 Stuart Hogg, 14 Tommy Seymour, 13 Huw Jones, 12 Sam Johnson, 11 Sean Maitland, 10 Finn Russell, 9 Greig Laidlaw (c), 8 Josh Strauss, 7 Jamie Ritchie, 6 Ryan Wilson, 5 Jonny Gray, 4 Grant Gilchrist, 3 Simon Berghan, 2 Stuart McInally, 1 Allan Dell.