Ernesto Valverde's Barca will take a slender lead to the Mestalla after Suarez's second-half header edged Valencia in the opening leg.
Barca dominated possession but they were unable to break through Valencia's packed defence until Lionel Messi clicked into gear, providing the assist for Suarez in the 67th minute as the visitors' resistance was finally broken.
"It's a minimal advantage that we have because there are 90 minutes left," Suarez told reporters.
"Valencia at home are always stronger and even more so in a Copa semi-final."
The result extended Barca's unbeaten run at home in the Copa del Rey to five years, having last tasted defeat against Real Madrid in 2013.
"What doesn't leave us calm is that they didn't cause us problems, this is important, it shows they respect us," the Uruguay international added.
"We had chances despite the little space we had, they had chances although they didn't go in."
Suarez has now scored 12 goals in his past 10 matches in all competitions and he added: "It's always important to help the team, today with another goal and we hope to continue like this."