Bath winger Banahan scored late on for England in Salta
England manager Martin Johnson was frustrated by the weak defending that cost his side victory in the second Test against Argentina in Salta.
The Pumas surged 21-3 clear shortly after the break when Horacio Agulla sliced through England's midfield and fed Gonzalo Camacho to score.
"The first try hurt us but it was the second-half one that really killed us," said Johnson.
"We wanted to win this game and we're frustrated because we felt we could."
Johnson was pleased with the way England fought back, inspired by the boot of Andy Goode, but disappointed not to complete a Test series victory after the 37-15 win in Manchester last week.
"This game was always going to be different from the first Test we won at Old Trafford because Argentina are a proud team, especially when they're at home," he said.
"You have to make them work a lot harder to score than that but the guys battled hard and played very well to come back in the second half.
"Argentina played with a lot of vigour as we knew they would. A few turnovers hurt us - it was always going to be like that early on.
"They took their chances better than we did.
"We played well last weekend, maybe the 37-15 scoreline flattered us a bit, but we really wanted to win this away game because we haven't done that this year."
Goode's fifth penalty kept England in touch but Juan Martin Hernandez slotted a drop-goal to keep the visitors at bay.
Bath winger Matt Banahan's late try gave England hope but the whistle came too soon as they lost 24-22.
"Matt played very well again. He took his try well and was good under the high ball. But ultimately we win and lose as a team," said Johnson.
I would have killed myself had we lost this game at the end
Argentina captain Juan Fernandez Lobbe
England captain Steve Borthwick added: "Without question we felt we could reel them in at the end.
"We believed throughout we could win. You could see that in the boys because they kept going.
"Credit to the way Argentina managed the game and frustrated us in the last few minutes. There were chances there for us.
"The way we built our score was great but we must take our chances and sustain pressure on the opposition.
"That's something we didn't do because the error count was too high."
Argentina captain Juan Fernandez Lobbe felt his side had avenged the first Test defeat.
"It was a really tough game," he said. "We wanted to change our image after what happened in the last match and we felt we achieved that.
"England are a very good team. We let them come at us in the third quarter but we held our nerve and are very happy with the result.
"I would have killed myself had we lost this game at the end."