The court ruled Hindus would get two-thirds of the land and be allowed to keep a makeshift temple that was built over the razed mosque's central dome.
In Delhi's Jama Masjid, the imam rejected the verdict. "If we do not get our rights we will never be able to walk in this country with our heads held high," said Shahi Imam Ahmed Bukhari after Friday prayers.
"It is our responsibility to maintain the peace, but we will not be broken, we cannot be broken. If the Supreme Court endorses the High Court's decision, I will urge all Muslims to consider the matter with all seriousness and concern."
But there were no reports of protests in Muslim-dominated areas, partly because people remained wary of inflaming public tensions in a country where Muslims account for only 13 percent of the 1.2 billion plus population.
Muslim groups said reaction was also measured because they still hoped to appeal in the Supreme Court and rebuild the mosque.
India is officially a secular nation and its top women's tennis star, its vice president and one of its richest men are all Muslim, as are some Bollywood stars and top ministers.
But such high-profile success stories mask the real status of Indian Muslims, who are some of the poorest in the country. Since the partition of the country in 1947 amid mass ethnic cleansing, there have been periodic riots between Hindus and Muslims.
Muslims account for fewer than 7 percent of public service employees, only 5 percent of railway workers and there are only about 30,000 Muslims in India's 1.3 million-strong military. Some fear the mosque verdict may yet turn into a recruitment tool for home-grown militants who have been blamed for a series of bomb attacks in Indian cities in recent years.
"There will always be a few hotheads who will try to exploit this verdict," said Amulya Ganguly, a leading political commentator based in New Delhi.
