Lionel Messi scored twice and set up Ousmane Dembele in a 3-0 win for Barca at Camp Nou that sent his side into the quarter-finals 4-1 on aggregate.
But former Germany international Ballack felt Chelsea were unfairly treated by referee Damir Skomina, who rejected a penalty appeal when Gerard Pique challenged Marcos Alonso in the box, with the score at 2-0.
"Same old story #referee," Ballack wrote on Twitter, seemingly referring to the infamous semi-final between Chelsea and Barca in the 2008-09 Champions League.
On that occasion, Chelsea felt wronged by a series of controversial calls from Norwegian official Tom Henning Ovrebo, who told the media he received death threats following the match.
Ballack was playing for Chelsea as Ovrebo rejected a handful of penalty appeals made by the Blues, who were eventually knocked out by a dramatic late goal scored by Barca midfielder Andres Iniesta.
The 41-year-old later offered a more clear-minded assessment of the game on Wednesday, writing: "Messi made the difference."