Bremen pile pressure on Benitez
The Germans, already eliminated after failing to win a match in their group until Tuesday, struck three times and hit the woodwork twice as the sluggish Italians looked nothing like the side that won the trophy last season.
Inter finished the group stage second behind Tottenham Hotspur, who drew 3-3 at Twente Enschede, when a win against Bremen would have been enough to put them top.
Spaniard Benitez, who took over after Jose Mourinho won the treble last season and then left to coach Real Madrid, had already had some close shaves this season.
The defeat means they have now lost seven games in all competitions, as many as in the whole of last season under Mourinho.
Club boss Massimo Moratti said recently that, in the past, he would have sacked Benitez for such a bad run but he was less trigger-happy these days.
Inter's performance against Werder, albeit with a largely second-string team, will do nothing to improve Benitez's standing with his president as his team are also far from convincing in the league, lying in fifth place after losing to Lazio 3-1 at the weekend.
With his eyes on the Club World Cup in Abu Dhabi later this month, the coach opted to rest several key players including Dutchman Wesley Sneijder.
The side were also missing Argentine striker Diego Milito through injury and defender Lucio with influenza.
"This was a match where we had already qualified. For me it is different. The important game was the last one with Twente," Benitez told Sky Italia.
"We tried young players and we did not risk more injuries. I do not believe my future depends on the World Club Cup."
The Germans, also far from spectacular this season, took a deserved lead through Sebastian Proedl's header in the 38th and doubled it with Marko Arnautovic four minutes after the restart.
Claudio Pizarro added another goal two minutes from time after Bremen had rattled the bar twice late in the game with a Per Mertesacker header and an Aaron Hunt shot.
Bremen have never lost to an Italian side at home in 15 matches.
With top Champions League striker Samuel Eto'o absent from any offensive move, all Inter could produce was a Goran Pandev cross that accidentally hit the post in the 66th minute and a shot that rattled the bar with the last kick of the match.