The South Americans, playing in their first World Cup quarter-final, came close to reaching the semi-finals in a dramatic and chaotic game at Ellis Park stadium in which both sides missed penalties.
"We could have made it into the semi-finals, that's the feeling that I have," said Martino.
"We've played with all our heart, we lost the game at the very end. We played with Spain on an equal footing but it was not enough in the end."
Spain had to work harder than expected to break through Paraguay's defence to make it to the last four at the World Cup for the first time since 1950.
Forward Oscar Cardozo, who failed to convert a penalty that would have put Paraguay in front, said he felt some responsibility for the defeat.
"I feel a bit guilty personally because of the missed penalty. If I'd have scored, I think things would have been different," he told reporters.
"But we feel at ease with ourselves because we gave it our all. We made history and we played really well. We're going with our heads held high."
Striker Roque Santa Cruz said the South Americans had been unfortunate.
"We played a great game but we lacked a bit of luck."
When asked about his future, coach Martino dodged the question, saying it was not the time to think about whether he would stay on.
"With or without me, there will be a new phase," the Argentine said.
"It was a game where we showed we could have come out winners. Now we have to resign ourselves to this tough blow."
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