Four goals not enough for Germany coach Low
The world champions headed into the match on the back of a stuttering start in Group D, featuring a 2-0 defeat in Poland and a 1-1 draw at home to the Republic of Ireland.
Nevertheless, much of the pre-match talk centred on whether Germany could beat their own record European win of 13-0 against San Marino in 2006.
It was a mark they rarely troubled despite a brace from Thomas Muller inside the first half hour.
"I am far from satisfied," said Low, who saw World Cup final hero Mario Gotze complete the first-half scoring in Nurnberg before Yogan Santos' own goal proved the only blot on a superb second-half showing from Gibraltar.
"The team has not lived up to expectations and requirements. If we want to play like a champions, then four goals are simply too few.
"We wanted to permanently occupy the penalty area, which was not the case - especially in the second half.
"It is always important to play against such teams in the width and depth; we often played in the middle.
"I would have also thought that some more players would impose [themselves]. The level that was present before and during the World Cup has dropped."
By contrast, Gibraltar coach Allen Bulla hailed an improvement few expected from a team that has already suffered 7-0 losses to Ireland and Poland during its first major international campaign.
Their wait for a maiden competitive goal goes on, although Liam Walker had Manuel Neuer scrambling with a magnificent long-range volley on the stroke of half-time.
"For us it is a great result, one that we needed to get going again," Bulla said.
"[Losing] 4-0 against the world champions is very good for us.
"We had a solid defence and we knew what Germany would try.
"We may be the smallest nation in UEFA but we have played quite well."