The right-hander dealt with elbow swelling during spring training after he missed the Indians' postseason run because of a broken hand.
His dominant outing Saturday night likely calmed any concern.
"I admit we had some anxiety just because he didn't pitch that much, but coming out of the chute he's been good since his first start," Francona said. "Now he's stretched out where the game dictates when he comes out as opposed to maybe a pitch count."
Carrasco allowed three hits while pitching eight scoreless innings as the Indians beat the Chicago White Sox 7-0 to extend their winning streak to five games.
The Indians have shut out the White Sox on back-to-back nights after Corey Kluber limited them to three hits in a complete-game shutout Friday.
Carrasco (2-1) struck out eight and walked one while throwing 106 pitches.
He admitted he wanted to take the mound for the ninth.
"I want to stay, but he's the manager and makes the decision," Carrasco said. "It's part of the game and nothing I can do about that. It's fine."
Francona was thinking about the future.
"It was cold," Francona said. "For him to try to pitch a shutout, he was going to get out over 120 (pitches). We need him for the long haul. My heart was saying, 'Yeah,' but it didn't make sense."
Brantley's two-run shot was his third home run of the season. Ramirez hit his fifth home run, a solo shot in the ninth.
The White Sox haven't scored in 23 consecutive innings. Tyler Saladino had two of their three hits.
To add to the White Sox's offensive woes, two injuries occurred. After reliever Zach Putnam issued a leadoff walk in the seventh, he exited with right elbow tenderness, the team announced. Manager Rick Renteria said the injury is affecting more of his triceps area.
Left fielder Melky Cabrera also left during the inning after hitting the wall while attempting to make a catch. He was removed for precautionary measures, and X-rays on his left wrist showed no fracture, the team announced. He is day to day.
Jacob May had his first career hit while pinch hitting for Cabrera in the seventh. The single ended an 0-for-26 streak.
"Fingers crossed, thank you, Lord," May said. "When I saw it go through, it was a little unfortunate we were down in the game but exciting at the same time."
While their offense struggled, the White Sox also got a short outing from veteran starter Mike Pelfrey (0-1). He was filling in for right-hander James Shields, who went on the 10-day disabled list Friday for a strained right lat.
Pelfrey was 0-2 with a 7.50 ERA in two starts at Triple-A Charlotte after he signed with the White Sox as a minor league free agent. In 11 previous seasons in the majors, he was 65-91 with a 4.57 ERA with the Mets, Twins and Tigers. Detroit released him at the end of spring training.
Renteria hoped Pelfrey could pitch five innings, and he lasted 4 1/3. He allowed four runs and four hits.
"When we talk to our guys, we talk about making sure that we back our guys, our pitchers," Renteria said. "That no matter what's going on offensively that defensively we still take care of business. I think he gave us a chance"
Encarnacion put the Indians ahead in the first inning with a two-run, 415-foot home run, his third homer of the season. Brantley scored after hitting a two-out single and stealing second.
The Indians added two unearned runs in the fifth for a 4-0 lead.
NOTES: The White Sox purchased the contract of RHP Mike Pelfrey from Triple-A Charlotte. ... The White Sox reinstated C Geovany Soto from the 10-day disabled list and moved OF Charlie Tilson to the 60-day DL before Saturday's game. Soto went on the DL April 13 for right elbow inflammation. Tilson went on the DL April 2 due to a stress reaction in his right foot. ... RHP James Shields went on the DL Friday for the first time in his career. He said his lat strain is "very mild." ... Indians manager Terry Francona said 2B Jason Kipnis may get a day off Sunday. Kipnis (strained right rotator cuff) was activated from the disabled list Friday. ... Francona celebrated his 58th birthday on Saturday.