Germany began their World Cup preparations with the match against the 154th-ranked Malta, with striker Cacau scoring twice - suggesting he could be the solution to his country's problems up front.
The Brazil-born Stuttgart forward netted either side of half-time with a powerful header and a well-timed strike.
Both of Löw's first-choice forwards, Lukas Podolski of Cologne and Bayern Munich's Miroslav Klose, have struggled for form this season with just five Bundesliga goals between them.
Cacau worked tirelessly and nearly finished with a hat-trick as one of the few fringe players who took their chance to shine.
But Löw was unimpressed by his side's lack of goals in a mediocre performance against a team who managed just one goal and conceded 26 in their own fruitless attempt to qualify for the finals.
"We came up short on goals, that was too few," said Löw. "We created a lot good opportunities, but were too casual in our finishing."
Germany were missing captain Michael Ballack plus their Bayern and Werder Bremen stars who are on cup duty this weekend.
Ballack's Chelsea face Portsmouth in Wembley's FA Cup final on Saturday while Bayern take on Bremen in the German Cup final at Berlin's Olympic Stadium, but only Cacau and Hamburg's Piotr Trochowski stood out in their absence.
Cacau's forward partner Stefan Kiessling, who hit 21 Bundesliga goals last season, had a game to forget as he failed to connect with the ball on at least five occasions with the goal at his mercy.
This was a fairly poor Malta side, ranked 154th in the world, who welcomed back veteran defender Massimo Grima after a five-year hiatus, but the 30-year-old struggled for fitness and his side never tested the hosts.
"It was a very good experience for my team as they are not used to playing at this level," said Malta coach John Buttigieg.
"I am not quite satisfied with the result as we conceded two goals through counter-attacks."
With the game won, Löw brought on 21-year-old defenders Mats Hummels of Dortmund and Leverkusen's Stefan Reinartz for their first caps, but Löw has already said they are part of a group who will not fly to South Africa.
"Some young players put in positive performances," said Löw.
"But we now have to work very hard. As for our missing players, we must take it as it comes.
"However, we will put in some good work in the two weeks before the World Cup."
Cacau opened the scoring when Hamburg's Dennis Aogo whipped in a cross and he powered home his header on 16 minutes.
Löw blooded Borussia Dortmund's striker Kevin Grosskreutz and he used his first touch of international football to find Podolski whose back pass was smashed home by Cacau on 58 minutes.
After the match it was revealed Grosskreutz is out of World Cup contention as he needs a knee operation.
Valletta defender Kenneth Scicluna then tapped the ball into his own net to compound Malta's woes and make it 3-0 on 60 minutes.
After this weekend, Germany will hold two training camps, one in Sicily and one in the Italian Alps, and will face Hungary in their second warm-up game on May 29 in Budapest.
The 27-man group will be cut to 23 for the official World Cup squad and Germany will play their final warm-up against Bosnia-Herzegovina on June 3 before flying to South Africa on June 6.
The Germans have drawn Australia, Ghana and Serbia in Group D with their first game against the Australians on June 13 in Durban.