Bilic added: "He had a big chip on his shoulder but Frank has proved his critics wrong.
"He has shown that he was always a great talent."
Lampard, 28, has admitted himself that he had doubts about his ability after he failed to score in Germany this summer as England went out at the quarter-final stage.
But Bilic has revealed he was shocked by the defensive nature of England's play at the tournament and that Lampard, who will win his 50th cap against Croatia, was not the only player to blame.
"The whole team failed and Frank didn't play up to his level," said Bilic.
"It is very difficult for the stars because people get used to you scoring week in, week out.
"For me, during the World Cup, he looked - as most of the English players did - not only tired but mentally and physically exhausted.
"They were very important games but you cannot doubt his ability on the basis of three or four games.
"The level he has been playing at in the last three or four years - week in, week out - is unbelievably good.
"He is not a robot that can always keep such great form.
"He was a little bit in a crisis but sooner or later, definitely sooner, he will be back on track."
England and Manchester United centre-back Rio Ferdinand was also at West Ham during Bilic's spell at the club - when current Portsmouth boss Harry Redknapp was at the helm.
"In both Rio and Frank you could see straight from the start that they had technique, character and everything to become players who were good enough to play for England," added Bilic.
"I said seven or eight years ago, when I told Rio and Harry, that he should be in the top three centre-halves in the world.
"I used to stay with Rio after training to show him things and practise a little bit.
"He, for me, is now - and especially for the last five or six years - among the best four or five defenders in the world."
Bilic believes England have a number of world-class players but is keen to expose the weaknesses displayed by them during the World Cup.
"I am not exactly going to tell you what these weaknesses are but, in general, they have great individual players - only in a situation like the World Cup they didn't play as a team.
"That is what they are missing and lacking - and I still think they do not play like a team."