Chelsea had just won the quarter-final replay at 2-1 at White Hart Lane on Monday and Lampard was celebrating in front of the Chelsea supporters when a fan ran on to the pitch and took a swing at him.
"It did shock me," Lampard told reporters on Tuesday as he prepared for England's Euro 2008 qualifier against Israel on Saturday.
"Fortunately I saw it coming and was prepared for it and luckily ducked out the way. It wasn't as bad as it could have been as an incident. But I hope that doesn't happen to me or anyone else again.
"It was strange. It was awkward, someone running at you like that... Fans have come on the pitch before but not with that kind of aggressive nature.
"Emotions run high and I don't want to stand here and criticise too much."
But he added: "Of course, the measures need to be taken to make sure it doesn't happen again.
A Football Association spokesman had earlier described the scenes as "totally unacceptable" and said the FA would be contacting Spurs "as a matter of priority."
Lampard is now looking ahead to the game at Ramat Gan on Saturday, where England need to make up lost ground in Group E.
Steve McClaren's men have dropped five points and slipped to third in the group after drawing with Macedonia and losing to leaders Croatia.
Difficult though it will be in Israel, compared with the game four days later against Andorra, Lampard believes England can have no excuses and need to make their ability and experience count.
"I hope we'll learn the lesson from Croatia because we didn't play as well as we should have done and we lost," Lampard said.
"We're full of players who have played in these atmospheres before -- Champions League, England games -- we've got the experience. So there's no excuses.
England have seven points, one behind Russia and three adrift of Croatia. Macedonia, who have played a game more, and Israel, are behind McClaren's men only on goal difference.
