As the celebrations began at Murrayfield on Saturday evening, one member of the Edinburgh camp expressed satisfaction with the result but expressed reservations about the way it had been achieved.

There may have been an element of psychology – for both internal and external audiences – in observations such as that from Michael Bradley, their head coach, when he said: "We're going to go to the Aviva [Stadium in Dublin for the semi-final against Ulster] and we'll enjoy the day, but we'll enjoy the day even more if we win the match, and still more so if we win the match playing the rugby we're capable of."

Bradley would always want to be seen to be asking more of his men, while also ensuring that prospective opponents think they may have even more to deal with than that which confronted Toulouse on Saturday.

Mike Blair, their vastly experienced scrum-half, could be interpreted as having taken a similar line with his observation that "we didn't play well, but we did a lot of good things".

Elaborating on it, though, Blair, who also played in all, and started most, of Scotland's matches when they were whitewashed in the recent Six Nations Championship, noted that ". . . in terms of flow of the game, we didn't have that real flow".

Lee Jones, his team-mate for Scotland and Edinburgh, struck a similar note when he said: "If I'm honest, I don't think we played at our best; I think we could have been a lot better."

It all seemed to carry an echo of the sort of philosophy players were exposed to in that failing national team camp.

Many of the same players were afield when Scotland faced France on the same pitch a few weeks earlier in a match that flowed in a very different way to Saturday's.

Scotland scored twice as many tries against France as Edinburgh did against Toulouse on Saturday, just as they scored three when losing what was another great game for neutrals to watch in Paris the previous year.

Before this match, those of us who had witnessed every one of Scotland's 14 meetings with France this millennium – they have recorded a solitary victory – and most of Edinburgh's 10 previous Heineken Cup meetings with Toulouse – they too had produced just one win – pointed out that another match that flowed as prettily would only suit one team.

Edinburgh have, of course, been much more effective than Scotland when it comes to crossing the opposition line, most notably when scoring six tries in the game of games in which they beat Racing Metro in their pool match.

It is also fair to note that it is not only in his first Heineken Cup campaign as a coach that Bradley has demonstrated how happy he is to encourage the sort of flamboyant style that Edinburgh like to regard as their hallmark. The stunning five-try win by his Scotland A side over England Saxons the night before the Calcutta Cup match which kicked off the Six Nations campaign remains the solitary highlight in a miserable couple of months of international rugby for Scottish observers.

However, Edinburgh have shown a capacity to change their style to suit the needs of each situation, while history has shown that the knockout stages of the Heineken Cup are not a time when matches flow unless, as happened in Dublin on Saturday when Leinster routed Cardiff Blues, it is all very one-sided. The other three fiercely contested quarter-finals produced a total of five tries.

Nathan Hines, the former Scotland lock who picked up a winner's medal with Leinster last season and has now set up an intriguing meeting with his former club after playing a hugely influential role for Clermont Auvergne as they progressed to a first semi-final, outlined just what these matches are about at the weekend.

He is the one team-mate of Blair's from the day Edinburgh played their only previous Heineken Cup quarter-final in 2004 who can pull rank in such matters on the scrum-half who has captained both club and country, and he was quoted ahead of Clermont's domination of the English champions, Saracens, as saying: "Leinster's match against Toulouse last season was the fastest and hardest game I'd ever played."

Blair touched on the same thing on Saturday when he mused: "I was wondering whether Toulouse are better than France . . . but that's not for me to say."

The quality of imports Toulouse can add to the nucleus of the France national team, the time they spend together and the ethos built at a club that has had the same head coach throughout the professional era would suggest they are, indeed, superior to France.

Yet they were beaten because Edinburgh put effectiveness ahead of philosophy, which surely reinforces the message that any nonsense that has been put into players' heads about a particular way they should be trying to play should be dismissed.

Never mind the flow of the game, the best teams know that winning is about playing to their strengths in a way that prevents opponents from playing to theirs.

Edinburgh did just that in magnificent fashion against Europe's finest team on Saturday.