The two nations went head-to-head in the first of two friendlies in Luque on Friday, with Paraguay edging the visitors 2-1 with all three goals scored inside the final 21 minutes.
A goal-line handball from Victor Yotun handed the Paraguayans a late penalty, which Derlis Gonzalez - a late substitute - stepped up to convert.
Bengoechea said his side should not have conceded the corner that lead to Oscar Ruiz's header - which Yotun was forced to raise an arm to keep out of the goal.
"We generated a corner [for Paraguay] and there came all [our work undone]," Bengoechea said.
"Paraguay has a good passing game and took advantage in the final minutes."
Of Peru's performance, Bengoechea added: "I really enjoyed it. The first half was as expected. We defended well, we had space and controlled the ball.
"In the second [half], [we] missed that because Paraguay went looking [for a goal]."
Peru's last hosting of Paraguay saw them win 2-0, but the latter have won their past two meetings.
Victor Genes' men snapped a four-match winless run with their late success over Peru, and will hope to build on it ahead of the continental competition in eight months' time.
