Salom, 24, was taken to a hospital after the crash where he underwent surgery.
The world champion said the team must become "more united than ever before" in an attempt to ward off growing threats from rivals.
Hamilton had been 43 points behind Rosberg before Monaco, the showcase race that every driver wants to win, but ended the weekend only 24 adrift and with everything to play for.
Sahara Force India picked up 23 points from the race with German Hulkenberg finishing sixth to grab eight points to add to Perez's 15.
The incident reversed the team`s fortunes after the Spanish Grand Prix where the two Mercedes drivers collided on the opening lap and gifted victory to debutant Dutch teenager Max Verstappen.
Red Bull`s Australian driver Daniel Ricciardo, who started on pole, came in second with Mexican Sergio Perez of Force India completing the podium.
The qualifying effort was Force India's best of the season so far.
His best lap in one minute and 13.622 seconds was enough to beat both Mercedes drivers comprehensively.
Tyre suppliers Pirelli`s introduction of a new `ultra-soft` compound for the special demands of the Mediterranean street circuit.
To endorse Red Bull`s revival, Ricciardo`s record-breaking teenager team-mate Max Verstappen was fourth-fastest just behind Rosberg.
Rosberg, winner for the past three years in the principality, was second fastest in 1:15.638 on the new ultrasoft tyres.
Bianchi, 25, died in hospital in his home town of Nice last July after suffering serious head injuries when he crashed into a recovery crane at Suzuka during the October 2014 race.
Championship leader Rosberg, 43 points clear of Hamilton after five of 21 races, remained cagey about what was said.
The seven-time Formula One world champion suffered traumatic injuries after hitting his head against a rock while skiing in Meribel, France in December 2013.
Championship leader Lorenzo made the most of the opportunity to claim his third win of the season and second in a row, to extend his advantage in the riders` standings over Honda`s Marquez to 10 points.
I don't think there's anything called form. It's about how you feel on that particular day. It's about how good you're mentally.