Speaking to Bild on Monday, Löw said "what has been said in public by some of my professional colleagues was in bad taste - especially the way in which it has been done.
"Criticism between colleagues should be done directly with the person concerned. That's the way we've always done it at the German Football Association (DFB).“
Neid had been criticized by Bundesliga coaches such as Colin Bell (Frankfurt) and Bernd Schröder (Wolfsburg) before the defeat to England.
On the list of complaints stood questions over the system the team played, the players' technique and mental strength.
Bickering between coaches at the national and club level was re-ignited by comments Neid made after Germany's exit to England in which she complained about the "catastrophic“ condition that her players were in when they reported for national duty.
Responding to Neid's comments, Frankfurt manager Siegfried Dietrich questioned why she had praised the players' fitness earlier in the tournament.
Finally beating Germany
A 108th-minute penalty kick by Fara Williams gave England their first ever win over Germany and a third place finish at the Women's World Cup on Saturday.
The 1-0 victory after 120 minutes of gritty battle at Edmonton's Commonwealth Stadium gave the sixth-ranked 'Lionesses' their first win over the European champions on their 21st attempt.
It also helped bury the heartache of the injury time own-goal by defender Laura Bassett which had ended their title bid during a 2-1 semi-final loss to defending champions Japan.
"It feels a lot better to be sitting here after that than it did the other day," said England coach Mark Sampson.
"To bounce back from what was a real, real blow for us, it's an incredible result for the team.
"We knew the challenge we faced today from a world class Germany team.
"I'm just incredibly proud of all the players and staff, to achieve a third place finish, to go home as the top European nation, to finally beat Germany, it was a real big statement for us today.
"It's something that these players will be remembered for forever."
The third place play-off had gone into extra time after the teams were locked 0-0 at the end of 90 minutes.
But England were awarded a penalty just minutes into the second period of extra time after Lianne Sanderson was pulled down by Tabea Kemme.
England 'no surprise'
And Williams slotted in past former world goalkeeper of the year Nadine Angerer, who playing her final match for Germany, dived the wrong way.
"It didn't surprise me as we have seen what England could do over the course of this tournament," said Neid after the match.
"They really wanted it today, they were very clever in their game."
Germany, winners in 2003 and 2007, lost 2-0 to the United States in their semi-final.
England had never gotten past Germany with their most recent loss a 3-0 drubbing at Wembley Stadium last year during which World Cup top scorer Celia Sasic scored twice.
England skipper Steph Houghton did well to back clear a goal-ward bound shot after just nine minutes in an evenly matched first half.
The defender, who had just received treatment for a painful ankle knock, lunged to clear after Jo Potter headed past her own goalkeeper Karen Bardsley following a Bianca Schmidt header across goal.
Within a minute Sasic had a chance to extend her tournament leading six goals but her weak shot was held by Bardsley.
Forward Ellen White headed over the bar after 26 minutes, and Germany's Sara Daebritz missed a chance to break the deadlock just before halftime but Potter blocked her shot.
After the break Germany had the best scoring chance on 53 minutes when Sasic crossed to Daebritz whose volley was kept out by a diving Bardsley.
Eniola Aluko came off the bench on 61 minutes and had a solo run towards goal three minutes from time but Angerer recovered the ball.
But England continued to push with Jill Scott failing to finish with only Angerer to beat, while Williams saw her goal-bound effort cleared by a defender.
But the game was finally decided with the clocking ticking when was Kemme was judged to have pulled down substitute Sanderson, and Williams scored from the spot.