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]."
Paolo Hurtado and Luis Ramirez are in doubt for the rematch in Lima, after being substituted at half-time due to fitness concerns.
Peru's last hosting of Paraguay saw them win 2-0, but the latter have won their past two meetings.
Both sides are bound for the Copa America in Chile, starting in June, and will not be drawn alongside one another as they are in the same pot ahead of the draw later in November.
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.
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