As the fall took place outside of the 3km mark, riders held up in the fall were not given the same time as stage winner Jasper Philipsen (Alpecin Fenix) and the rest of the peloton.
Yates came over the line 31 seconds down, while Carthy lost 38 seconds. Both riders had already lost more time than most of their GC rivals on stage 1 when Primoz Roglic (Jumbo Visma) stormed to victory and the first red jersey in this year's race.
The crash on stage 2 appeared to take down riders from Bora-Hansgrohe and Burgos-BH but it also caused a major split in the main field.
Roglic and Egan Bernal (Ineos Grenadiers) survived the fall and finished safely in the first group but the time losses for Yates - who came into the Vuelta with genuine GC hopes of his own - and Carthy - who was third last year - seriously dents their hopes for the overall.
Yates is now 56th overall at 51 seconds, with Carthy down in 76th at 1:11.
They weren't the only riders to lose time, with Lucas Hamilton (BikeExchange) also losing 31 seconds. Louis Meintjes (Intermarché-Wanty-Gobert) and Jack Haig (Bahrain Victorious) lost 38 seconds, while David De la Cruz (UAE Team Emirates) lost 1:11 and Pavel Sivakov (Ineos Grenadiers) 1:15.
Thank you for signing up to Cycling News. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.