The Colombians were narrowly beaten by the hosts on Friday night as a 2-1 loss saw them exit the tournament.
"Obviously we're not going away happy," Ospina told FIFA.com. "Losing is never nice, especially when you've gone toe to toe with the hosts.
"But I think we can be satisfied with what we've done at this World Cup, in going further than Colombia have ever done before, something that will always stay with us."
Brazil's reward for beating Colombia is a semi-final showdown with Germany.