Sweden will start as underdogs when they meet England in the final World Cup Group B match on Tuesday.
Alexandersson scored Sweden's equaliser against England in 2002
But Sven-Goran Eriksson's side will have to upset the record books if they are to beat their manager's compatriots for the first time in 38 years.
Swedish midfielder-turned-right-back Niclas Alexandersson told BBC Sport his team can cause England a shock again.
"We prefer being underdogs. We are more relaxed and don't have as much pressure on us when we play them," he said.
When the draw for the World Cup finals was announced on 9 December, there were many smiles from the England camp, particularly on the face of Swede Eriksson.
But there would have been knowing grins from the Swedish contingent because of the Scandinavians' recent record against the English.
THIRTY-EIGHT YEARS OF HURT
The 11 games since England last beat Sweden:
1979 - DREW 0-0 (friendly)
1986 LOST 1-0 (friendly)
1988 DREW 0-0 (WC qualifier)
1989 DREW 0-0 (WC qualifier)
1992 LOST 2-1 (Euro 92)
1995 DREW 3-3 (friendly)
1998 LOST 2-1 (Euro qual)
1999 DREW 0-0 (Euro qual)
2001 DREW 1-1 (friendly)
2002 DREW 1-1 (WC 2002)
2004 LOST 1-0 (friendly)
The last time England managed a victory over the Swedes was in 1968 when Martin Peters, Bobby Charlton and Roger Hunt were on the scoresheet in a 3-1 win.
And when the two sides line up in Cologne, the Blagult (blue and yellow) as they are known, will again fancy their chances of upsetting the English.
Alexandersson, who plays for IFK Gothenburg, told BBC Sport: "It seems like even though we have this good record against England, we still come up as underdogs every time.
"There has never been any pressure on us to beat them and we have always done better when that is the case.
"We prefer being the underdogs as we are more relaxed and don't have as much pressure on us when we play them.
"The expectations are higher for England. They won't be happy unless they are in the semi-finals and that will work as an advantage to us.
Sweden have bonded work rate with big-name stars
"We have raised our standards when we played against good teams. It will be more of an open game now."
Alexandersson scored Sweden's equaliser in the 1-1 draw at the 2002 World Cup in Japan and has re-established himself as a regular in coach Lars Lagerback's line-up.
And the former Everton, West Ham and Sheffield Wednesday utility man is confident the current squad have the star quality to provide a shock in this year's tournament.
He said: "We know if we have a good day we can beat any team.
"The difference with Sweden now, compared to five or 10 years ago, is that some of our players are playing in the biggest clubs in Europe, not just in England but with Zlatan Ibrahimovic at Juventus and Henrik Larsson at Barcelona.
"We have players in top clubs that have become individual stars in their own right and we haven't had that for a while.
"Before, it was always based on team spirit and hard work with no stars. Now we have famous players with experience of playing in the Champions League.
"That takes away a bit of our respect for the big countries and those players also know what it's like to play against the big players each week.
"Our players know how to play against them and get used to coming up against them."
Sweden fans still hold Sven-Goran Eriksson in high regard
Eriksson is still highly thought of in his homeland and Alexandersson is relishing the latest encounter with his countryman.
"There is always a lot of hype and build-up when we play against Sven, but once you get on the pitch you don't think about it too much. It's like playing against a good friend.
"I think the criticism of him has been unjust as he has got a good record in his matches.
"If you look at the managers who have been before him I don't think they had that direct criticism on him, and the high expectations on England make it hard for anyone to manage them."
Eriksson is still in search of his first win over his homeland after two friendly draws and the World Cup stalemate in Japan.
And he knows he must overturn an impressive record and a bullish Sweden camp if he is to return home with his pride intact.