Hodgson steered his team through an unbeaten campaign that ended with them taking top spot courtesy of six wins and four draws following Tuesday's triumph, sealed by goals from Wayne Rooney and Steven Gerrard.
Anything other than a win would have left the 1966 world champions in second place but England finished on 22 points, one ahead of Ukraine who crushed San Marino 8-0.
"You can imagine quite a few emotions are churning around inside me," Hodgson said. "I died a thousand deaths every time they crossed the halfway line.
"I will put on hold my thoughts about what we are going to do in Brazil until a later date," he added, referring to the 2014 finals. "I am, though, naturally delighted we completed the job."
Rooney grabbed his 38th goal in his 86th international with a 41st-minute header scored without his protective headband on.
Skipper Gerrard then ended all fears of a Poland fightback in the 88th minute with his 21st goal on his 107th appearance.
"It was very fitting Steven Gerrard scored the goal that put the game beyond doubt," said Hodgson, "because if anyone has played a captain's innings throughout these 10 games it has been him."
The Liverpool midfielder, who said before the game he was still haunted by England's 3-2 home defeat by Croatia in November 2007 that put them out of Euro 2008, was also a happy man.
"We are delighted with the result but they made us work very hard for it," said Gerrard. "We were determined not to suffer what we went through after we failed to reach the Euros in 2008.
"Now we can prepare for the World Cup and that is a great feeling. I know Wayne and me scored the goals tonight but it was a collective effort and many players have played their part over the last two seasons to get us here."
Rooney is now 11 goals shy of Bobby Charlton's all-time England record tally of 49.
"It was good to score again after scoring against Montenegro on Friday. I've been scoring for Manchester United this season too so that's great," he said.
"We've proved we can live with the pressure. We have put in two good performances and I think it was enjoyable for the fans and everyone is delighted we are going to Brazil."
Young Tottenham Hotspur midfielder Andros Townsend, who netted on his debut in the 4-1 win on Friday and had another superb game against Poland, said he was taking nothing for granted despite having had two good games for his country.
"I know I have to stay at this level or play better because there are a lot of players who want to play for England," he said.
"I am not even thinking about that though. I've got a hard enough job keeping my place in the Tottenham team, we've got so many fantastic players there."
Poland manager Waldemar Fornalik, who could lose his job this week, said his team did not take their chances especially in the first half when Robert Lewandowski screwed the ball across the face of Joe Hart's goal from the type of chance he normally buries for Borussia Dortmund.
"We created the chances but we did not take them and we have done that throughout the campaign," he said.
"But England are a very good team and they are getting stronger and stronger. They look better and better in every match and I think they will be among the contenders for the title in Brazil."