Roy Hodgson's team booked their place in Brazil next summer with a 2-0 victory over Poland at Wembley on Tuesday.
England went into the final two games knowing only wins over Montenegro and Poland would be enough to guarantee qualification.
Despite the pressure, they managed to play with a freedom that has often been lacking and created a host of chances in both matches.
Everton pair Phil Jagielka and Leighton Baines both played their part, and Martinez said: "What pleases me is the performance as a whole.
"I think they had a very tough test - in football the hardest thing to do is achieve results you are expected to have.
"The pressure was immense and the way that the England team performed was sensational.
"I was pleased to see our players contributing, enjoying their football and having a massive role in that game."
West Ham boss Sam Allardyce was particularly excited by the emergence of Tottenham winger Andros Townsend on the international stage.
He said: "I was absolutely delighted obviously and I think both performances warranted the wins they got, and the Poland game should have been won more comfortably.
"I was delighted to see the emergence of Andros Townsend and just how well he played in both the matches. Going forward hopefully they will keep everyone fit and will probably use the next group of friendlies to try out more and more youngsters.
"We can look forward to the summer now I'm glad to say. We were all a bit nervous about it but we have delivered and that is what matters."
Hull manager Steve Bruce praised Hodgson for his tactics and selection.
"I'm like every other Englishman," said Bruce. "I thought we were fantastic in the last two games. A big pat on the back must go to Roy.
"It was a big call to play Townsend. He also went for it in terms of the attacking team he put out. We should all be praising him as a manager and a coach.
"We're all delighted England are going to be at the World Cup and we can look forward to the draw then to being there in June because Rio is some place."
Norwich boss Chris Hughton has urged those players in contention to use the rest of the season to show they deserve a place.
"There's a lot of football to be played," he said.
"That's the exciting part. I think what's happened over the last week and what has raised everybody's excitement levels is the manner in which the two games were won, in a very exciting manner.
"It's a long season and we all know what can happen over a season. Form is up and down, nobody will want to get injured at any stage of the season.
"The important thing for the England team and for those that qualify for England is that they're there. It's up to every player then to prove over a season that he's worthy of getting on that plane."
Southampton boss Mauricio Pochettino believes England can win the World Cup and would like to see Hodgson's men take on his native Argentina in the final.
He said: "I think England has great football players that can do well.
"I think England is a candidate to win the World Cup, but it depends a lot on the fitness of the players, especially that last month before the tournament starts.
"Also how they are playing at the end of the season, so I think that is a very big factor on how England would fare at the World Cup.
"I would love to see Argentina and England in a final. Why not?"