Celia Sasic equalized from the penalty spot in the 84th minute and Germany won a shootout 5-4 to defeat France in quarter-final action at the FIFA Women's World Cup before 24,859 mostly pro-French spectators at Olympic Stadium on Thursday.
The Germans advanced to a semifinal on Tuesday in Montreal against either the U.S. or China.
"I think from our perspective it wasn't the best match," Neid said through an interpreter. "We can play better.
"We had to fight hard in the second half just to get into it. That showed the character on our team. But France is a very good team. They are skilled, very fast, tremendous control of the ball."
The French wasted numerous chances before Louisa Necib scored in the 64th minute against the two-time Women's World Cup champions.
In the shootout, all five Germans scored, while France scored on its first four attempts until Nadine Angerer stopped Claire Lavogez on the final shot.
"The last player, I felt she might have been scared and I was lucky I chose the right side," said Angerer.
French coach Philippe Bergeroo elected not to blame the referee, Canadian Carol Anne Chenard, for calling a penalty against his squad and placed no responsibility on Lavogez.
"It was more that the goalkeeper made the stop," Bergeroo said. "It's true we dominated the game, but we wasted a lot of chances that would have given us the answer.
"It's always a problem when you play well and have three or four chances and don't score."
Germany, winners in 2003 and 2007, will play in a fifth semifinal in its last seven Women's World Cups.
The game between top-ranked Germany and third-ranked France had been called an "early final," but the French, who beat the Germans 2-0 in a friendly in October, controlled much of the play and had most of the scoring chances.
France nearly scored in the opening minute when Necib one-touched a cross from Elodie Thomis just wide.
They finally struck when Jessica Houara played a high ball into the penalty area that went off a defender to Necib, whose shot changed direction off Babett Peter's foot and left Angerer no chance.
The Germans got it back when Chenard pointed to the spot after Leonie Maier's pass at the edge of the penalty area was blocked by Amel Majri's outstretched arm.
Sasic slotted in her tournament-leading sixth goal.
Canadian defender Rhian Wilkinson tweeted during play that it was an "epic game" and added: "What a showpiece for the women's game!"
The excitement continued into extra time, when France missed a glorious chance with three minutes left when Gaetane Thiney couldn't handle a cross from Houara with the right side of the net gaping open.
But once it went to the shootout, there was a sense of inevitability.
"I had a good feeling because we managed to fight back and we got into the shootout," said Neid. "And I know what our players can do on penalties. They want to do it."
German star Anja Mittag, with five goals in the tournament, was substituted at the intermission by Dzsenifer Marozsan. Neid said it was because she wanted her team to have more possession of the ball "instead of running after it."
Peter was playing in place of defender Saskia Batusiak, who was suspended one game for yellow card accumulation.
ESPN Stats reported that Germany is 12 for 12 all time in penalties at the Women's World Cup.