The two nations were locked at 1-1 following 120 minutes of football in their last-16 tie, and Russia triumphed 4-3 on penalties to shock the 2010 world champions in Moscow.
Fabregas, who has made over 100 appearances for Spain but was left out of their squad for this summer's tournament, has said that Russia "had a plan" to take the game to a penalty shootout, and it ultimately "paid off for them".
"I am speechless because I expected a different game today. I think Spain is a much better side than Russia. Russia had a plan which was to go to penalties and pray, and it paid off for them," Fabregas told BBC Sport.
Chelsea midfielder Fabregas has won one World Cup and two European Championships with the Spanish national team.