England's performance was criticised by a number of former players including Gary Lineker, who branded the showing by Roy Hodgson's side as "awful".
But Chelsea midfielder Lampard, who earned his 100th cap for the Three Lions in Kiev, is confident England are more than capable of topping their qualifying group to secure their passage to Brazil.
"Playing two games at home and with the way we have been performing there lately, I fancy us to do it," Lampard said.
"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."
England were without the suspended Danny Welbeck for the game against Ukraine as well as injured strike duo Wayne Rooney and Daniel Sturridge.
Lampard believes Rickie Lambert did well leading the line in their absence and feels England will be a stronger team when they return to the fold.
"I thought Rickie Lambert did very well holding the ball up last night and he worked his socks off - he's got real quality," said Lampard.
"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."