"There are other strikers who need the team, but he is one of those - as (Cristiano) Ronaldo is and (Lionel) Messi is another - strikers who can create goals for themselves."
Steven Gerrard insisted that Ibrahimovic's fourth goal in Sweden's 4-2 win, an overhead kick from outside the area, was the best goal he had ever witnessed at a stadium.
The giant Paris St Germain striker issued an ominous warning to Trapattoni's Ireland team, who travel to Stockholm next March for a make-or-break World Cup qualifier.
Having won his 100th cap for England, Gerrard compared the Sweden striker's goal to the overhead kick scored by Wayne Rooney for Manchester United against Manchester City in February last year.
"It is the best goal I have seen live," Gerrard said. "I think the best goal I have seen before that was Wayne Rooney's.
"Everyone knows how special that was but this one tonight - an overhead kick from 25 yards when the ball is six feet in the air - only certain players can do that. And he is a special player.
"I have mixed emotions. Obviously I am very proud for myself, getting to 100 (caps) and really pleased with the lads for large parts of the game.
"I thought we controlled the game and did not look like losing it but sometimes you have to hold your hands up to an individual special performance.
"I congratulated him after that. He said some nice things about me before the game which was really nice and if I could return the compliment - that was one of the best individual performances I have seen. He is not everyone's cup of tea but he is certainly mine."
Before last night, Ibrahimovic had scored four times against English opposition in 1,536 minutes. His four goals came in the space of 71 minutes. Roy Hodgson said that his six second-half substitutions contributed to England throwing away a 2-1 lead in the last 12 minutes.
"We kept them at bay, asked them questions and our passing and movement were good. But I made further changes in the last 15 minutes and unfortunately that's when Zlatan decided to step into the picture and win the game for them. The fourth goal was the crowning glory, a fantastic goal."
Ibrahimovic said that the first goal of the four meant the most to him because it was the first scored at the new Friends Arena. "The first goal I liked more because it was an historic goal."
Hodgson, meanwhile, insists he has no fears over the form of goalkeeper Joe Hart.
Almost since the 2010 World Cup, Hart has seemed like the one player England cannot do without.
Yet mistakes that have crept into his game at Manchester City have spilled onto the international scene as well. Last night, there were a couple of minor errors in addition to two major ones, the last of which allowed Ibrahimovic to score his jaw-dropping fourth. "We are not bothered about Joe Hart," said Hodgson.
"He is a very good goalkeeper. We think we will have a lot of success with him in the goal even if tonight it wasn't maybe one of his best days, this happens in football."
Unfortunately, they reckoned without Ibrahimovic. Earlier this week, Gerrard was asked to mark his international career out of ten. "Six or seven," said the Three Lions skipper. The same question was posed of Ibrahimovic last night. His answer was "ten."