When Stroustrup invented C++, he wanted C++ to be compatible with a complete language with sufficient performance and flexibility for even the most demanding systems programming. He “had a perfect dread of producing yet-another pretty language with unintentional limitations.” See Section 2.7 of The Design and Evolution of C++ for historical details.
At the time, Stroustrup considered C the best systems programming language available. That was not as obvious then (1979) as it later became, but Stroustrup had experts such as Dennis Ritchie, Steve Johnson, Sandy Fraser, Greg Chesson, Doug McIlroy, and Brian Kernighan down the corridor from whom he could learn and get feedback. Without their help and advice, and without C, C++ would have been stillborn.
Contrary to repeated rumors, Stroustrup was never told that he had to use C; nor was he ever told not to use C. In fact, the first C++ manual grew from troff source of the C manual contributed by Dennis Ritchie. Many new languages were designed at Bell labs; in “Research” at least, there were no rules enforcing language bigotry.