Pedro's 19th minute strike at the San Siro had seemingly set Pep Guardiola's side on their way to a second successive final appearance.
However, Jose Mourinho's men hit back through Wesley Sneijder's strike on the half-hour, before second half efforts from Maicon and Gabriel Milito inflicted a first defeat by more than one goal on Barca since Guardiola took charge nearly two years ago.
And both Pique and Pedro hit out at official Olegario Benquerenca, accusing the referee of favouring the Italians for several key decisions, ranging from awarding both of Inter's second and third goals to yellow-carding Barca right-back Dani Alves for diving rather than giving the La Liga outfit a penalty.
"I have been seen it on TV and you can see that Milito's goal was offside and Maicon's came after a foul on [Lionel] Messi," Pique said in Sport.
"We got nothing from the officials. The second leg has to have an impartial referee. Inter knew us very well, they dominated the game and they knew how to stop our game."
Goalscorer Pedro told As: "He has not managed things well because he has interrupted much of the game and that's a shame."
"It's always difficult to lose for those who aren't used to losing. I'm like that too. It's the characteristic of a team which always wins," he said.
