The Spanish champions are in Germany on Wednesday for the first leg of their semi-final clash against the Bundesliga outfit.
"You have to hope Real have a bad day, but if they're on form and do what they normally do, then your chances of beating them aren't very high," he told Bundesliga.com.
"Dortmund are a great team, but I think Real have better players and are a better side overall. If Real play well and are consistent, then I think they're favourites to go through.
"I'm a Real Madrid fan and I have been all my life and I think they're a notch better than Dortmund, but in the group stages this season you could see that they could compete and they even beat them here in Germany."
Carvajal is a graduate of Madrid's youth academy and joined Bayer in 2012 after failing to break into Los Blancos' first team.