Sir Clive Woodward and Graham Henry traded verbal barbs after New Zealand sealed a 3-0 series win over the Lions with a 38-19 victory in the third Test.
Lions coach Woodward, who led England to World Cup glory in 2003, said: "The only time you can judge teams is when you arrive at World Cups.
"I'd just caution New Zealand that they will also have good days and bad days.
Henry, who led the Lions in 2001, hit back by saying: "It's very pleasing to win 3-0, I think it was 2-1 last time."
The pair have been at loggerheads since 2001, when Woodward was highly critical of Henry when the New Zealander was put in charge of the 2001 Lions for the tour to Australia.
Henry also came under fire during and after the tour as the series, which ended in a 2-1 defeat for the Lions, was plagued by reports of internal division.
"The 2001 tour was a very good series," said Henry. "There was some great rugby played. Both teams scored seven tries each.
"I don't know what the try count was for this series, I've lost count.
"But 2001 was a blessing for me because I wouldn't be sitting here now if it wasn't for 2001.
"So I should thank the people for the ribbing because it pushed me back to New Zealand quicker than I probably would have come back."
Woodward tried to stress afterwards that the New Zealand public should not get carried away with the whitewash and reminded them that the All Blacks have not won a World Cup since 1987.
"I don't think there is a gulf between the northern and southern hemispheres," he said.
"All I would say, and I'm saying this in a positive way, is for all New Zealanders to be very reflective.
"The only time you can judge teams like New Zealand is when you arrive at World Cups when everyone has had the same degree of preparation.
"I would offer a caution on the New Zealand team. When I see them going through the quarter-finals and semi-finals and win a World Cup, then it is time to celebrate, because it is a very tough tournament.
"Reputations can be destroyed in one game when you're at this level."
Henry, however, paid tribute to the Lions players and insisted that the tours should continue.
"They must survive, I think the Lions brand is something special and every time they tour it's a major occasion," said the former Wales coach.
"They've had some great teams over the years and the players in those countries still see it as their peak of their rugby careers to be selected for the Lions.
"It would be very disappointing if that was taken away. I think it's essential the Lions continue because they'll have great teams in the future.
"I think they did their best. I think the All Blacks played some quality rugby, a different style which the Lions found difficult to handle."