Richie Gray damaged his bicep and looks likely to miss the rest of the Six Nations while Luke Crosbie injured his shoulder and looks set to miss next weekend's match with France.
Scotland Head Coach Gregor Townsend said in The Scotsman: "They're both in a lot of pain. Richie knew straight away that it was a bicep injury, so that doesn't look good for this championship.
"Luke's is a shoulder injury which is a painful one now but that might settle, though probably not for next week. Let's hope he's not done any significant damage there. It's a blow to lose two players who are in our starting team. Richie is a very experienced player for us and Luke has been outstanding this season and took the game to Wales.
Townsend admitted Scotland ending their Cardiff hoodoo was tempered by the way his team allowed a 27-0 lead to be cut to a single point in a 30-minute spell.
Townsend pointed to the high penalty count and two yellow cards - for George Turner and Sione Tuipulotu - that left the Scots hanging on as Wales scored four second-half tries.
Tries from Pierre Schoeman and Duhan van der Merwe saw Scotland go into the break 20-0 ahead. Van der Merwe then scored again early in the second half with a fine solo effort but Townsend was alarmed at the number of penalties his side conceded.
"To score those two tries was a really good reward - sometimes you don't get that in first halves, but to have that cushion should have made it a more comfortable second half," said Townsend. "The fact that it didn't is a concern for us. A lot of that was to do with the penalty count and the numerical advantage Wales had for 20 minutes. That created problems and created pressure and Wales played their best rugby in that period, too.
"I don't think it was anything to do with a change of gameplan. We went out in the second half with the same mindset but we couldn't get on ball and had to defend a man down."
Scotland conceded 16 penalties to Wales' four, and three of the Welsh ones came in the first seven minutes.
"Yeah, crazy stats," said Townsend. "It was nine penalties against zero in the second half - Wales didn't concede a penalty in the second half. Sixteen penalties to four in a game we were 27-0 up in just doesn't seem to make sense but we've got to look at where we can improve.
"We were getting penalised for things around the tackle ruck area and offsides that Wales weren't getting penalised for. We have to be better. To concede 16 penalties, no matter if we thought they were harsh decisions, it's going to put you under pressure, and it did."