Rúben Vinagre had already been dismissed by referee Anthony Taylor for planting his studs high on the shin of Swansea winger Nathan Dyer in the first half.
But the Manchester-based official also showed red to Dutch midfielder Fer for bringing down Hélder Costa from behind as he looked to launch a counter-attack for the Championship leaders.
The foul appeared worthy of yellow, but Taylor - who was also caught in controversy after his refereeing performance for Arsenal's 2-2 draw with Chelsea on Wednesday, brandished red to leave both sides down to 10 men.
It had no impact with neither side unable to find a winner, leading to a replay, but Carvalhal felt that Taylor was wrong to send Fer off.
Asked for his opinion on the dismissal, he said: "Don't ask me about the first because I didn't see it. The situation with Vinagre, I didn't see.
"But the second [red] is a classic yellow card. Foul in the middle, not in the area or a goalscoring situation. It is a foul from the back but it is not a kick for a red card. It's a tactical foul. It's a yellow card.
"We will analyse it. It looks like we will appeal because I understand also that when the journalists ask me this, it seems like that they understand it is a yellow card also.
"When it's this common, I believe we have reasons to appeal, so we will probably do that."
Carvalhal encouraged by performance
Swansea were second-best for significant periods of the game with back-up goalkeeper Kristoffer Nordfeldt forced to make three strong saves inside the first 30 minutes alone.
But Carvalhal felt that his side took another forward step in their development with their performance at Molineux.
This was the Portuguese manager's third game in charge of the Swans, having won, lost and now drawn - in that order - since his appointment on December 28.
"I'm very pleased about my players because the commitment and attitude was good," he continued. "Part of the game, we played with good quality against a very strong team with a good dynamic.
"We blocked the dynamic of them but they are, since the beginning of the season, moving that dynamic and they create problems to us. We created problems for them also.
"After I arrived, two days after we play against Watford and we win, three days after we play against Tottenham and we never lose that game in normal circumstances. And after four days, we prepare a team to face the most strongest team in the Championship.
"I'm very happy about my players because I felt that we progressed to another step today. And as you understand, in these circumstances, playing two days, three days, four days, we are recovering.
"To use a new dynamic, a new formation and new ideas in this short time, I'm really very happy. The players are completely under my expectations because I believe that we've progressed because we are better for the next game."
We didn't want a replay, admits Swans boss
The draw means the two teams will have to clash horns again later this month at the Liberty Stadium, adding another fixture to the Swans' congested schedule.
Carvalhal admitted that an extra game to play was the last thing he wanted, but chose to focus on the positives of the performance and vowed that his side will give the replay their all.
"I don't wish to play more games because we need training," he admitted. "It is not our main competition. Of course we are more interested in staying in the Premier League. It will be very tough work for all of us.
"We are in the cup but today if you ask me at the end of the game if I take the positives about the game, I will say that we progressed because it was a clean sheet and because we played better quality in parts of the game.
"So I think the team is progressing but if you ask me if I want another game, I didn't want that. I would prefer us to focus on the Premier League and trying to stay in the league.
"More games is not much welcome but we will do our best next game."