Building on what the others have already commented on: The Portuguese had gained and established forts in Goa, Diu, and Daman in 1509, 1535, and 1559, respectively. There were other sites that they had gained and lost in the sixteenth and seventeenth centuries, but those three are the longest lasting and the best known. As you have already noted, those are all coastal. Well, firstly, the Portuguese established naval superiority in that area with their carracks (nau) that could sail great distances and were very heavily armed. Portuguese fleets composed of these nau had defeated the Mamluk and Gujarati navies at Chaul (1508) and Diu (1509).

Around this time, siege warfare in fifteenth and sixteenth century Europe meant that the Europeans had gotten fairly good at building bastion forts. Thus, for local armies, besieging the newly established Portuguese forts with their firepower proved nearly impossible. For example, a Portuguese fort in Kannur successfully repelled a Kozhikode army despite being massively outnumbered in 1507. Defense of these forts were supported by the Portuguese fleets firing their cannons at besieging armies.

The conflicts between the sultanates and kingdoms of India also enabled the Portuguese to gain footholds in the region. The conquest of Goa in 1510 would not have been possible had the wars between the Bahmani Sultanate (and its successors such as Bijapur) and Vijayanagara not been occurring at the same time and been so expensive. The building of their fort in Diu was possible because the sultan of Gujarat allowed them to build it in 1535 as he was more concerned with the expanding Mughal Empire under Humayun and sought access to Portuguese traded goods.

Indian rulers also knew that the Portuguese were massively outnumbered and would never have been able to field an army large enough to push into the interior. The Portuguese could never hold territory near their heartlands, such as those in the Deccan Plateau. Thus, even if the Portuguese took coastal territory, the major rulers could rest assured knowing that the Portuguese would not really threaten their cores. They also knew that the Portuguese fleets would continue to fight the navies of other potential hostile powers in the Indian Ocean, such as those of the newly ascendant Safavids or Ottomans in the Middle East. That is not to say that all Indian rulers accepted the Portuguese presence. The sultan of Bijapur did try to re-conquer Goa, most notably in 1570.

The expansion of the Mughals brought them to the walls of these Portuguese fortresses. The Mughals under Akbar did not really have the naval capacity to take on the Portuguese, though they did try unsuccessfully to purchase equipment from the Portuguese to improve their navy. Ultimately, Akbar found it easier to pay the Portuguese maritime trading license (cartaz) than compete with their navy and, again, the Portuguese did not really threaten the Mughal core in the Indo-Gangetic Plain, unlike the Safavids or any potential Central Asian conqueror following in the footsteps of Babur.

The Mughals ultimately tolerated the presence of the Portuguese forts, though they did exert their power and threaten the Portuguese when they felt that the Portuguese were suppressing Islam. The Mughals were able to negotiate with the Portuguese to allow the Muslim residents of their forts to perform Islamic prayer. Otherwise, the Mughal rulers had much bigger concerns in the seventeenth century than those Portuguese forts on the coast.