Metro General Manager Richard S. Page yesterday defended the subway system's performance on Inauguration Day while acknowledging that Farecard vending machines in stations failed to sell tickets fast enough to meet the needs of unexpectedly large crowds of passengers.

As a result, station attendants opened the gates at times on Tuesday, permitting thousands of people lined up at the vending machines to ride free.

Page said at yesterday's Metro board meeting that "we did experience a few difficulties." He acknowledged that "our Farecard system is a hard one to use," but said he would not recommend that Metro revert to the method sometimes used at special events of collecting cash fares in barrels.

Page said he did not know how many people the system carried on Tuesday -- an earlier rough estimate was 160,000 -- and added that the system efficiently carried large numbers in and out of the city. He had no estimate of the revenue lost because of the emergency opening of gates.

Also at yesterday's meeting:

Page said that it will cost Metro $7.5 million over a period of six years to replace the fasteners that hold Metro's tracks to concrete. That has been the most expensive of three track-wear problems Metro has discovered. A new, long-lasting fastener has been found. Additionally, Page said it will cost $2.5 million over seven years to replace fastener anchor bolts. The third problem is excessive rail wear on curves, for which various rail-saving techniques will be tested, Page said.

Metro announced it will put on sale by the end of the month two new maps of Metrobus routes -- one for routes in the District and Maryland, the other for routes in the District and Virginia. They will cost $1 each and will be available from Metro and from drugstores and convenience stores.

The board elected Fairfax County Supervisor Joseph Alexander as chairman for 1981, succeeding Cleatus E. Barnett of Montgomery County.