He worked hard, ran around a lot, but his goals did not prevent Cologne from being relegated, and the club he left to join Liverpool, Bayer Leverkusen, are a sort of German Newcastle United - remembered for the trophies they nearly won rather than any they put in the cabinet. And if the Kop recalled him at all it would have been as part of a Leverkusen side ripped apart on Liverpool's march to the 2005 European Cup.
A 25-yard shot driven spectacularly into the top corner that should all but ensure Liverpool's qualification for the Champions League proper was the best rebuke to those who believed the man with the pony-tail would be, by a distance, Benitez's fourth-choice centre-forward.
"You saw - on a pitch that was not good - the quality he had. And there was extreme heat," said Benitez. "Andrei is a striker with different qualities to the others I have signed. He is very intelligent and I know that some people were suspicious because he was a free transfer but I thought he could surprise them."
Benitez's counterpart, Elie Baup, whose trademark is his baseball cap, commented that what struck him about Liverpool was their almost mechanical organisation. Benitez had quipped the one thing Liverpool had not been able to control had been the sun.
Toulouse imagined that kicking off when the heat was at its most shattering might prove one of their few advantages, but these days, just as muddied pitches are not the great levellers they once were in the FA Cup, so the sun burned down on both sides with the temperature 37F.
Peter Elmander, whose goals had taken Toulouse into this Champions League qualifier and who last weekend had overcome Houllier's former club, the French champions, Lyon, was largely reduced to long-range, impotent efforts.
What would have been perhaps the only concern to Benitez with a potentially decisive meeting against Chelsea looming on the horizon is his captain's fitness. Steven Gerrard lasted just under an hour, which, in the heat, was all his manager would probably have given him. But early in the game, Gerrard appeared to have a toe stamped on and spent much of his time on a burning pitch in discomfort. On their return to Merseyside, there would be a scan and an anxious wait.
There will be little anxiety at Anfield as the second leg approaches. Benitez's fourth Champions League qualifier went much like the first three, in that Liverpool achieved a near knockout blow in the first round of the tie.
To qualify for the competition proper Toulouse knew they had to win on this island on the Garonne, where Glenn Hoddle's England had been ambushed by Romania during the 1998 World Cup.
Toulouse produced nobody with a better sense of rhythm than Carlos Gardel, the man who invented the tango. And it was fittingly an Argentine, Javier Mascherano, put in the afternoon's most committed display; expending the kind of sweat to be found in any tango bar in Buenos Aires as dawn breaks.