The American, who is riding for the Belgian team as a stagiaire for the remainder of the season, fell heavily and despite finishing the stage with cuts all over his body was taken to hospital for surgery on several deep wounds.
Twenty-four hours after being on the operating table a bandaged Costa was at the finish of stage 4, watching on his teammates rolled over the line.
"I hope or tomorrow or the day after I can be back on the bike," he optimistically told Cyclingnews.
"It's just road rash really on my abdomen and nothing is broken. I hope to continue my plans to race with the team. I've got two races next week with the team. I'm super anxious to get back on the bike and this is such a super opportunity they've given me."
Costa came down on stage 2 when he hit a cat-eye in the middle of the road. He was feeding at the time and was the only rider to fall. He crossed the line 23 minutes down on his teammate and stage winner, Julien Vermote.
"As soon I as got up there wasn't a thought of not continuing. I was a bit dizzy to start with but got back up and finished in the gruppetto. That was fine but really sucked was that I had to wait in the hospital quite a while for my surgery. I was an emergency list but they kept getting cases in front so I was only operated on, on Tuesday evening."
"They were pretty deep cuts, all the way down to the bone on my elbows. They would have been too painful to clean and stich up if I had been awake so they knocked me out. I don't know how many stitches that I needed but I don't think that it were that many. They cuts were so deep and they had been sitting there for a whole day so they'd already started to heal in places."
"When I heard that Julien won the stage I was super excited and I was really looking forward to being there until the end of the race. It unfortunately wasn't meant to be."