Suarez joined Atletico last summer for only around €11 million in add-ons following six seasons at Barcelona, as incoming boss Ronald Koeman deemed the Uruguayan striker surplus. He went on to bag 21 league goals, including match-winners in each of Los Colchoneros' final two La Liga outings.
"It was a joke," Alba told Cadena Ser, according to ESPN's Sam Marsden and Moises Llorens. "He is someone who gave a lot to Barcelona and they practically gave him away for nothing, above all to a direct rival in Atletico."
It proved to be a consequential decision for all involved parties.
He added: "And look, they went on to win the league with him. I didn't like it. Aside from the friendship we have, where are you going to find a striker like him? It is difficult to find one. Yes, there are some very good players, but what Luis gave us."
"He won the league and shut a lot of mouths," Alba said. "His last year wasn't easy at Barca and he has had the chance to shut some people up."
Alba and Suarez collected four league titles and a quartet of Copa del Rey crowns in six years together, adding to the former's impressive trophy haul at the Camp Nou.
The Spanish international defender said Suarez's influence was missed this past season.
"I can tell you that the atmosphere (at Barca) with Luis was spectacular. He is a guy that works hard, that was great for the group, and the numbers speak for themselves: (he is) the third-highest goalscorer in Barca's history," Alba said.
In the end, Suarez proved to Koeman and other doubters that he's still capable of being the focal point of an attack.
"I had to live through a difficult situation, starting the season being underappreciated and Atletico opened the door to give me the chance to show that I could still be a force," Suarez said in May after his side finished seven points clear of third-placed Barcelona.