The Brazilian-born centre-back has underlined he has a good relationship with his defensive partner and added he expects the club to fight for silverware
Their relationship has been called into question after Carvalho abandoned Portugal's training camp last week prior to the Euro 2012 qualifier against Cyprus.
The 33-year-old said he felt disrespected after learning Pepe would start instead of him and retired from football shortly after leaving the camp.
It has been rumoured that their relationship may be damaged, but Pepe has poured cold water on the speculation.
"Many people envy Real Madrid," Pepe told the club's TV channel. "I have no problem with Carvalho. This was a situation that happened with the coach.
"He is a great person, a friend of mine and he has made great things in football. He is a role model. We have to respect that."
Pepe stressed there are no problems on the team and said he believes the club can push for glory.
"There is a very good atmosphere," Pepe noted. "We have a very good squad. Madrid are the biggest and we have the best team. This is a very good side who will fight for all the titles.
"We are showing after every match that we are doing well and I have a very good feeling. Never before have I had bigger hopes than this year.
"We are doing very well, we are training well and we are like a family. If something happens, we always have a friend to help us and that is very important in a club."