The 31-year-old was denied from 12 yards by Eiji Kawashima after Keisuke Honda's handball had given Fabio Capello's side the perfect chance to equalise 10 minutes into the second half.
He wants to retain the responsibility in South Africa, although he admits Capello will have the final say. "It's down to the manager," the Chelsea player told ITV1. "I'll always want to take it. It wasn't a great penalty. It's disappointing because I've practised loads this week. I'm always confident in taking them and that will make me go away and work harder. If the manager wants me to take it I'll always step up."
The miss did not prove costly, with own goals by Marcus Tanaka and Yuji Nakazawa overturning Tanaka's opener. Overall, Lampard was pleased with the final work-out before heading out to South Africa. "It was not an easy game," he said. "It was not a vintage performance by far but it's about players and the team trying to find their way a bit."
Reflecting on today's result and Monday's 3-1 win over Mexico at Wembley, he added: "We've played two and won two. We have to take positives from that.
"It's down to the players. We've stepped up our game. In the first half we were slightly sluggish, and in the second half we got more of the ball and got the ball into their box more quickly," he added.