Low: We need to improve
The Germans open their Euro 2012 campaign in Group B against Portugal in Lviv, Ukraine, on Saturday 9 June, but after losing two of their last three games, Low's side boosted flagging confidence against minnows Israel.
A first-half goal from Bayern Munich striker Mario Gomez put the hosts ahead before Leverkusen's Andre Schuerrle came off the bench to double the lead eight minutes from time with a superb long-range strike.
Having suffered a shock 5-3 defeat to Switzerland in Basel last Saturday, the Germans managed to avoid their third straight defeat of the year, after also losing to France in February, but must still improve, according to Low.
"It was a pretty decent final test, this will give us some momentum," he said. "Not everything ran smoothly, but taking a victory into next week will do us good. We still have to improve and work on finishing our goal chances, the organisation was better, but there is still much to do."
"We have sensational quality in the squad, now we just have to show it," he said. "We had some good combinations. It can't always go perfectly, which is why the victory was important.
"The fact not everything worked today is normal, because we haven't played together for two weeks. We've showed in the last few years what that it does work and it's important we hit the ground running in our first game."
The 27-year-old injured his calf in Bayern Munich's UEFA Champions League final defeat to Chelsea a fortnight ago and sat out the win over Israel, but should be fit.
"Bastian has been pain-free since Wednesday," said Low. "Now he has to start to run and he will train with the team again by Tuesday at the latest."
Schweinsteiger, who has scored 23 goals in 90 appearances for Germany, suffered heart-break in the final as his missed spot-kick allowed Chelsea to win the penalty shoot-out, but is one of Low's first choice names.
Israel coach Eli Guttman is backing the Germans to live up to their pre-tournament billing as one of the favourites to lift the title in the Kiev final on 1 July.
"I am satisfied on the whole," he said. "Germany is one of the best teams in the world, it was normal that we had to defend well against such an opponent.
"This German team are among the favourites, even their bench is impressive. Germany can certainly do it at the European Championships."