Roy Hodgson's men moved a point clear at the top of Group H with a 0-0 draw in Ukraine on Tuesday night, but the performance at the Olympic Stadium in Kiev drew stinging criticism from former England striker Gary Lineker.
The ex-Tottenham forward, who scored 48 goals for his country, mocked England's passing and described the team's overall performance as "awful".
Lampard argues that a point in front of a hostile 70,000 crowd was not a bad result, especially when England were missing a number of their top players like Wayne Rooney, Daniel Sturridge and Danny Welbeck.
The only way that England will definitely qualify for Brazil will be if they beat Montenegro and Poland next month, but Lampard is confident that the team will be able to do it with their best attacking players available.
"Playing two games at home and with the way we have been performing there lately, I fancy us to do it," Lampard said.
"We will have to tackle that one in a month's time. The first thing here was not to lose and it was a shame that we couldn't win the game but we have to believe in ourselves that we can go and do it next month.
"We all know how difficult it is when you go away in competition football in the group games.
"Of course we wanted to win but you have to dig in sometimes and we did that in the second half.
Obviously we will be stronger for the options [when Rooney, Sturridge and Welbeck return].
"I thought Rickie Lambert did very well holding the ball up last night and he worked his socks off - he's got real quality.
"But the options you are talking about - when you are without Wayne Rooney and Daniel Sturridge, the form striker in the Premier League, then of course you are going to miss players like that.
"We will be stronger when they come back because you want to choose from all your fit players.
"Unfortunately, there will always be a couple of injured players at any stage in an England squad of 24 or whatever. The team have to react and get results like we did here."
Lampard became the eighth England player to reach the 100-cap mark last night.
The 35-year-old admitted it was a special night for him even though he missed a late chance to make it even more memorable.
Such is Lampard's self-deprecating manner that he did not want to spend much time talking about his achievement.
The England vice-captain spoke at length about the influence of another of his fellow centurions, though - Chelsea team-mate Ashley Cole.
Cole moved level with Billy Wright on 105 caps in Kiev and he used every ounce of his experience to stifle the pace and trickery of Ukraine forward Andriy Yarmolenko.
"I thought [Cole] was fantastic. He was our best player, in fact," Lampard said of the 32-year-old left- back.
"It's not always easy to manage everything on the pitch but he kept tight to their right-winger and didn't give him a chance to get a run in.
"The speed and fitness of him at his age is fantastic. He has great awareness - people talk about him going forward but defensively he is absolutely top drawer.
"He has done it many times for England, Chelsea and Arsenal before that. He really rises to the task of playing against top-class wide men.
"Ukraine had very good wingers last night and Ashley blocked them off straight away."
There was also praise from Lampard for another Chelsea team-mate, Gary Cahill.
"[Cahill] has been consistent in a lot of difficult games we have played - Champions League and Europa League finals," Lampard added.
"He has always stood up and performed fantastically well on those occasions.
"He has come on so much considering he has only been with us a couple of years and he has won a Champions League, a Europa League and is now first choice for England, so he definitely deserves everything he gets."