Sanchez, who plays for Barcelona, is the biggest star in Chilean football, but he comes from a poverty-stricken background.
He suggested in an interview with the Daily Express that England players, on the other hand, are "soft" because of their pampered lifestyles.
Speaking ahead of Chile's visit to Wembley on Friday, Sanchez said: "I learned to be tough, and you can only learn that if you grow up in the environment (I grew up in).
"England or other European teams they did not grow up in an environment like that, but having everything so easy made them soft."
England striker Lambert welcomed the barb.
He said: "You can't really buy motivation like that to be honest.
"It is his opinion, and we will take it on board and we will be looking forward to the game on Friday."
Lambert is one of three Southampton players in Hodgson's squad for Friday's game against Chile and the clash with Germany at Wembley four days later.
Uncapped duo Adam Lallana and Jay Rodriguez were also called-up for the double-header, and Lambert is delighted to see so many familiar faces within the international set-up.
"It is brilliant," said Lambert, who earned his first call-up in August at the age of 31.
"It is nice to have two boys from the team I play with week in, week out. It is strange showing other people around and showing them where to go. It has been nice.
"They deserve to be there. The way they have performed last season and especially this season, they have both been absolutely superb.
"All the English lads in the Southampton team have done well. Especially Adam and Jay. It is rightly deserved."
Southampton owner Nicola Cortese vowed to uphold the club's tradition of bringing through young talent from their famed academy when he bought the club in 2009.
The south-coast club are a beacon of hope for English football as they have produced a number of youngsters who have gone on to become top stars such as Gareth Bale, Theo Walcott and Alex Oxlade-Chamberlain.
Southampton are something of an anomaly though as the number of home-grown players making it in the top flight has dwindled recently.
Lambert thinks the answer would be to cap the number of foreign players in the Barclays Premier League.
Lambert said: "The number of foreigners should be limited. You should start playing with British-based players, definitely."
Lambert praised Cortese and Saints manager Mauricio Pochettino for investing time in home-grown players.
"The manger does (like to do that). It comes from Nicola as well, the chairman," Lambert added.
"He has made it clear that is the way he wants to go and that is the way he has driven the club.
"Since the gaffer has come in, it is clear to the young ones that, if you are good enough, you will get a chance."
Lambert wrote another chapter in his Roy of the Rovers story in August when he scored the winner for England against Scotland on debut at Wembley.
The journeyman striker is now an established member of Hodgson's squad and he is determined to prove he deserves to be on that plane to Brazil over the next week.
"I will try to continue to impress and, if I get a chance on Friday or Tuesday, whether I am starting of coming on as a sub, I will be determined to do well," the former Blackpool and Rochdale man said.
"(Going to the World Cup) is a possibility and that is what I am aware of.
"I know how hard it is going to be to get there. It is a long way away and I know how hard it is going to be."
Hodgson confirmed on Wednesday that Steven Gerrard will miss the game against Chile because of a hip injury.
That means Frank Lampard will skipper the side if he recovers from a slight cold which did not prevent him from training.
Lampard will be awarded a golden cap to commemorate his 100th appearance before kick-off.
Lambert is proud to be playing and training alongside one of only eight England centurions.
"He has been superb," Lambert said of the Chelsea midfielder.
"To be involved with players like Frank Lampard, Ashley Cole and Steven Gerrard, who have played over 100 caps, is an honour.
"You can see why they have got 100 caps when you train with them every day. They are top professionals and top players. It is full credit to him. He fully deserves it."