Paolo Guerrero's header in the second half was enough to seal a second Club World Cup title for the Brazilian outfit, even though Chelsea threatened with a number of late efforts on goal.
Lampard said that the players will leave Japan with a 'bad feeling' because of the amount of chances they wasted after going behind.
"It was always going to be a tough game, they're a very good team," he told BBC Sport.
"We've come away with that bad feeling that we had enough chances to at least draw the game."
"They're very organized, Brazilian teams in club football can be like that, they're very organized and they counterattack. We knew what they were going to bring and we knew it was going to be a tough game. We're just disappointed to get all the way here and not win it."
Chelsea's attention is now solely focused on domestic matters and Lampard insists the club must kick on despite this latest setback.
He continued: "We have to go and win a run of games in the league, keep ourselves in the hunt in the league, we've got the Europa League, the FA Cup, the Capital One Cup all coming up so we really have to keep pushing on everything."
The England midfielder also thanked the traveling Chelsea fans for making the trip to Japan to support Benitez's men.
"Absolutely fantastic - I said it after the first game, the way they supported the team," he said. "They were all in Munich to celebrate the best night in Chelsea's history. They follow us everywhere, they're the best fans."