Barca were stunned at the Parc des Princes as Angel Di Maria and Julian Draxler inspired PSG to a 4-0 victory in the first leg of the last-16 tie.
Laporta says that Bartomeu should have fronted up after the defeat and accepted responsibility for Barca's humiliation and was generally scathing of his tenure as president.
Speaking to RAC, he said: "You feel messed up [as president].
"The first reaction that comes into your head is to go out, send a message of recognition, look forward and live from repentance.
"It surprised me that Bartomeu didn't come out, the president of Barcelona. I haven't seen him anywhere.
"It's another test about what I think of him. It's been a while since this board started destroying Barcelona, the only thing they are doing is taking advantage of what we left and dedicating themselves to their own business, doing their own thing.
"It's dangerous to leave Barcelona in the hands of this board."
Bartomeu took over as Barca president in January 2014 following the resignation of Sandro Rosell.
During that time, Barca have won La Liga twice, two Copas del Rey and the Champions League.