Barcelona were far from their fluent best and had to rely on a Sebastian Coates own goal three minutes into the second half to claim a 1-0 victory in Lisbon on Wednesday.
The win saw La Liga pacesetters Barca move three points clear atop Group D following their 3-0 opening day win over Juventus.
Sporting bounced back well after the goal and could have claimed a share of the spoils late on through Bruno Fernandes, but head coach Valverde was impressed with his side's ability to keep the hosts at bay.
"If you want to win big games you have to suffer," he said
"We played with real determination and dominated the first half.
"When we went 1-0 up Sporting gritted their teeth and caused us a little insecurity. But, come on, this is the Champions League and it is never easy."
Sporting now face a daunting visit to Juventus in three weeks' time, but Valverde admitted he has seen enough to think they can still qualify from a difficult group.
"They are still one of our direct rivals and can get through," the Spaniard added.
"They play Juventus next and nothing has been decided in this section. They have players who play at a high level but what I like most about them is their group mentality. They also have a good coach."
Sporting acquitted themselves well throughout, and boss Jorge Jesus believes the Portuguese side have shown the rest of Europe that he has a team to be reckoned with.
"At the break I told my players we could beat Barcelona," he said. "I felt I knew what we had to do to win. We ended up losing to a freak own goal.
"Against the world’s second-best team, we performed spectacularly. We shut off all their main passing routes in the first half. In the second half we controlled the ball better.
"Having said that, it’s difficult to create big chances against Barcelona. I feel Sporting left a great image of an excellent team on the watching world."