MasterCard was intended to be a North American bank card, whereas Visa is international. While I encountered a number of merchants who readily accepted the Visa, few said they would accept MC.
The Cirrus network is one international network, but some ATM's in San Jose are on the Plus network, which means your debit card might not work. The best bet is to check with your bank prior to travel. You should be able to acquire a current Costa Rica ATM list for your bank's network.
During my two trips to C.R., I had to do a little searching to find an ATM which accepts my card. Fortunately, the Banco de Costa Rica (BCR) a block from both the Presidente and the Del Rey accepts both Cirrus and Plus network cash cards. The bank is located 1 block north of Hotel Presidente, one block west of the Hotel del Rey, at the corner of calle 7 and avenida 1, southeast corner. Numerous other banks also offer ATM's, as do the casinos. Here's a helpful hint: The ATM in the Colonial Casino does not dispense cash directly; rather, a receipt is issued by the machine, which you then take to the casino cashier to obtain your cash. This is very handy, as you can get the cash in whatever bill/coin denomination combination you choose.
Smart travelers will carry an ATM, a major credit card and perhaps a second ATM card from a different system, just to make sure.
I'm curious why you do not carry Visa?

Is there an advantage to carrying only MasterCard?