Smoak leads the Mariners with 13 home runs, but went 0-for-3 with two strikeouts Monday and saw his average drop to .189 overall and .141 in July.
"I think everybody has seen what's going on," Smoak said after learning of the decision from Wedge and general manager Jack Zduriencik. "It's one of those things where you go down there and get your work in and get back to where I was a couple months ago.
"It's a matter of getting that feel and finding something day-in and day-out that gets you to where you want to be."
Smoak was the American League Player of the Week in late May and hit five home runs in a 10-game stretch at one point, but hasn't put things together as the Mariners hoped this year at the plate.
"I believe in Justin Smoak. I believe he's going to be a part of this," Wedge said. "But right now we feel this is the right thing to do for him."
Carp just finished a 20-day Minor League injury rehab with Tacoma and will be activated off the disabled list after recovering from a lingering shoulder issue. He's been playing first base with the Rainiers and went 1-for-4 on Monday, putting his average at .220 in 15 rehab games with Tacoma.
The Mariners have one other roster addition to make as well, as Ichiro Suzuki's trade on Monday put the 25-man roster at 24 even before Smoak's demotion.
Wedge said the chance to work in a less-stressful situation could help Smoak find the stroke he's been looking for as a powerful switch-hitter who was regarded as one of baseball's top hitting prospects when acquired by trade from the Rangers in 2010.
Smoak understands that, though he clearly was shaken by the decision.
"You never want to get sent down," Smoak said. "You're definitely not happy. But it's something you've got to go through sometimes to get where you want to be.
"You take a deep breath down there. They don't have this every day," he said, nodding at the circle of reporters around his locker. "It's something where you can go down there and get your work in and do what you need to do to get better."
Smoak was sent down to Tacoma for a stint after his arrival in Seattle in 2010. When he returned for the final 14 games, he hit .340 with three home runs and nine RBIs. He doesn't take anything for granted, however.
"Baseball is baseball, big leagues, Triple-A, rookie ball," he said. "It's just one of those things where you've got to keep working. I've definitely shown I can play here and belong here, so it's just one of those things where I've got to go down there. I've got some work to do."