England had entered their final two qualifiers, against Montenegro and Poland, knowing that victory in both games would guarantee their spot in Brazil.
Roy Hodgson's side
defeated Montenegro 4-1 on Friday,
but with Ukraine thrashing San Marino in their final game on Tuesday, anything less than victory over Poland at Wembley would have sent England into a play-off.
"It has been a long couple of days since Friday. We had a lot of time to kill," Gerrard told BBC Radio 5 live.
"The tension has been immense, even in the game. At the back of your mind, you are thinking one mistake could put us in the play-offs.
"It was a relief, it was very emotional at times. We have had a lot of criticism, so to get over the line was a lot of relief."
England, under Fabio Capello, struggled to get through their group at the 2010 World Cup finals in South Africa and were then thrashed 4-1 by Germany in the second round.
Hodgson took over from Capello before the 2012 European Championships, where England were beaten on penalties by Italy in the quarter-finals.
Qualification feels great - Hodgson
That remains Hodgson's only competitive defeat, with England winning six and drawing four of their 10 World Cup qualifiers.
"It has been a collective effort over two years," added Gerrard. "The manager has created a great blend of youth and experience.
"We have proved there is hope. There is big confidence within the group. It is important to stay humble, as there is a long way to go."
who suffered a broken metatarsal before the 2006 World Cup in Germany, failed to score in either that tournament or at South Africa 2010.
"We have to focus now," said the Manchester United striker. "We are delighted, and hopefully all the players can stay fit.
"We've gone out and shown we're a fantastic team. We're excited. I think it's good times for England."
had marked his debut in the victory over Montenegro with a goal and again started against Poland, who were backed by 20,000 supporters inside Wembley.
"There was a lot of pressure to deliver, and we did that," said Townsend. "Poland had a lot of fans here. It was not like a home fixture, it was unusual.
"After the hype [of his debut], it was tough for me to keep the same level. If anything, I am happier with tonight's performance."
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