Pique, whose straight red card looked harsh from television replays, told local media the decision appeared pre-meditated, comments condemned by the head of the referees' technical committee, Victoriano Sanchez Arminio, who said he would be making a formal complaint.
It was the latest episode in a series of recent attacks by Barca and their great rivals Real Madrid and a weary-sounding Del Bosque said it been happening in Spain for as long as he could remember.
"The same thing has always happened, always, always," Del Bosque, a former Real player and coach, told Reuters.
"The advice is that the less you talk about referees the better but as they are not going to follow it the best thing is not to say much at all," he added.
Barca said on Monday they would appeal Pique's dismissal and club spokesman Toni Freixa told a news conference the Spanish, European and world champions had "not been having much luck" with refereeing decisions this season.
Last season, the majority of the criticism came from Real Madrid and coach Jose Mourinho was punished by UEFA for implying there was a conspiracy favouring Barca.
Del Bosque said Spanish football was enjoying one of the best moments in its history and called for tolerance.
"Things could change," he said in an interview at the football federation's headquarters outside Madrid.
"I believe that if there were a bit less tension and a bit more tolerance it would be better for everyone."
