The result temporarily moves the Catalans 14 points clear of Atletico Madrid at the top of the table, with only six matches left to play.
"It was more important that we picked ourselves up after a hard week and the players have showed great attitude today and stepped up. You want to repay them".
Next weekend they face Sevilla in the Copa del Rey final, too, as they chase a domestic double and Valverde called on the club's supporters to focus on the positives.
Does that win secure the title?
"I am optimistic [about the rest of the season], of course", Valverde added.
A rainy day and a subdued crowd of just 69,544 spectators - well short of the 99,354 capacity - was reflected in a turgid opening spell for Barca, until Suarez struck to break the deadlock and restore some cheer to the stands 15 minutes in. We knew the fans could be angry, but we're hurting, too.
The shock exit in the Champions League to Roma on Tuesday night still framed some of the dialogue.
Valencia, however, found a foothold and arguably were the better side by the end of the half.
GK Marc-Andre ter Stegen, 7 - His careless footwork reared its head again when his pass out was intercepted in the area by Rodrigo but he recovered by tipping the Spaniard's shot on to the bar.
MF Andres Iniesta, 7 - The captain dictated the pace of the game and was desperately unlucky not to score when his stinging volley was beat away by Valencia goalkeeper Neto.
Valencia got a late lifeline when Dembele brought down Jose Gaya and Dani Parejo scored a penalty which sneaked under Ter Stege, but there was no time for an equalizer.
Real Madrid nearly followed Barca out of the competition on Wednesday, as Juventus raced into a 3-0 lead at the Santiago Bernabeu to level the tie on aggregate, only for an injury-time penalty from Cristiano Ronaldo to send the holders through.