It marked the former Barcelona striker's third goal for the club.
"We knew the problems we were going to have against an opponent that always makes things tough, especially at their place," he said. "The important thing is that we won. We suffered at the end, but we won.
"I am really happy to have scored and that we won, which is what we wanted. Celta have players with a lot of quality and can be dangerous. But we kept the clean sheet, which was also important, were efficient in defence and took our chances."
For the first time, coach Diego Simeone paired Suarez with Diego Costa in attack.
"I feel good with Costa," Suarez added. "Everyone knows his importance and the years he's spent here at Atletico. We're trying to adapt to each other in the best way possible because we've never played together before."