De Gea was left writhing around in pain after an accidental collision with Traore in the second half of the 1-0 victory at Old Trafford on Tuesday.
The incident left United's goalkeeper struggling to breathe but he said he will be ready to face Villa on Friday.
"He's one of the strongest players in the Premier League so it was very painful in my arm and in my stomach but it was fine," De Gea said.
"We win the game, so everything's fine. I feel very well. It was just when I hit Traore it was painful. I couldn't breathe, but it was fine."
De Gea's pain was eased even further when Marcus Rashford's deflected effort handed United all three points in stoppage time. The Spain international also played his part in the crucial win with a stunning save to deny Romain Saiss in the first half.
The result means Ole Gunnar Solskjaer's team will start the new year second in the league table but De Gea has called for "calm" when asked about the possibility of a title challenge in 2021.
"I think there's belief," he added. "You have to believe, keep believing all the time. But at the same time we have to be calm because this is a long way to finish, many games to come.
"We have to be very focused on Aston Villa and then to the next game and then to the next game.
"I think now we have a winning mentality and this is very important for the team. All of us, we want to win, we keep trying until the end.
"The manager wants us to try until the end. It was great to see the team trying to score until the last minute and then we scored a goal so it's perfect for us.
"We have a massive three points and then now try to recover as soon as possible and be ready for the next game."