Vilanova, who was Guardiola's assistant at Barcelona, passed away on Friday after losing his long-running battle with throat cancer.
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Guardiola was visibly emotional during his side's 5-2 Bundesliga win over Werder Bremen on Saturday and spoke of his deep sadness at the passing of the 45-year-old former Barca coach.
Speaking after the game, Guardiola told reporters: "Tito was more than a friend. It was difficult to focus on the game today.
"I want to send my condolences to his father, Joaquim, his mother, Maria Rosa, his wife Montse, her daughter Carlota and his son Adrian.
"The condolences come from my parents, my family and my brothers as well.
"We were very young, we both wanted to conquer the world and we both did it. I can only say that the sorrow that I feel will stay with me all my life. It will be impossible for it to go away."
Vilanova led the club to the Liga title last season, though his tenure was heavily interrupted by his illness.
He was diagnosed with throat cancer for the second time in December 2012 and left Camp Nou after just a season in charge to undergo treatment.