The victory made it eight wins from eight qualifying matches for Fabio Capello's England team, who booked their ticket to South Africa next summer. Two goals from Frank Lampard, two from Steven Gerrard and one from Wayne Rooney made it 31 goals for England's rampant side, who head their section by seven points with two matches to spare.
A shellshocked Bilic, who had accused Capello of taking the Englishness out of the England side, said: "We didn't expect this in our worst nightmares. They were fantastic from the start. They didn't surprise us. They played their own game and they looked the sharper, more aggressive side even before the first goal.
"We were very happy at half-time that it was only 2-0. It could have been five. Our goalkeeper [Vedran Runje] was fantastic. When we conceded a third goal we could not come back. I would like to congratulate them for a fantastic performance."
And on the chances of England captain John Terry holding aloft the FIFA World Cup trophy next summer, Bilic added: "Based on tonight definitely. But it is not easy to play every game like tonight. They missed their first pass after half an hour. It was one-two, one-two. It was perfect. If they manage to play like this then of course they can win it."
The defeat means Croatia are locked in a battle with Ukraine for the runner-up spot in Group 6 and a place in the play-offs, which could yet be a route to South Africa. But it will take all Bilic's powers of motivation to lift the spirits of his side, who were missing key players, including Tottenham Hotspur's Luka Modric. Arsenal's Eduardo did manage a consolation headed goal in the second half - but it was scant consolation.
Bilic admitted: "We were totally down in the dressing room and we will be down for days. I can't find anything to hold on to. But luckily our next game is not in three or four days." In fact they play Kazakhstan in their last match in Astana on 14 October.
Bilic added: "We knew without four key players we are not near the same team, but we didn't expect the difference to be so big. But we have character. We are going to come back for our game against Kazakhstan."