Suarez volleyed in just before halftime but was correctly ruled offside, with the Uruguayan ranting furiously at the assistant referee in frustration.
They still remain unbeaten in LaLiga despite the disappointing draw against Getafe.
Valverde's men now find themselves with a rare midweek lay-off before returning to the field for a league match against Eibar on Saturday. Ernesto Valverde's side are nine points ahead of second place Atletico Madrid. "Our opponents defended really well and we were unable to score", Valverde told beIN Sports. "It is unusual for us not to score here at our stadium".
That pair were rarely overly troubled, but at the other end, Valverde's decision to bring both Paco Alcacer and Philippe Coutinho into the line-up did not have the desired impact.
France forward Ousmane Dembele was back in action for Barcelona after recovering from his most recent injury, entering the match midway through the second half. Former Arsenal midfielder Mathieu Flamini came on towards the end to make his debut for Getafe, who are 10th.
Pique played over 80 minutes in Thursday's win against Copa del Rey semifinal win against Valencia despite picking up a knee injury at Espanyol last weekend.
However, Maxi Gomez equalised before the break with a back-post header before his 12th goal of the season put the home side ahead with 10 minutes to go.
The result ended a run of six straight defeats in all competitions for Valencia. "He will come back bit by bit, but we think the game tomorrow (Sunday) is a good time for him to be there".
Girona missed a chance to open the scoring before halftime when Aday Benitez had his penalty shot saved by Sergio Rico.
The Spain midfielder ultimately came on as a substitute in the second half against Getafe and he could not inspire Barca to victory either as Getafe produced an impressive defensive display to deny the home side, something they nearly managed in the return fixture which they narrowly lost 2-1 after leading 1-0.