The manager has found himself under even more pressure in the wake of the 2-1 loss in Cardiff, which leaves the Scots second-bottom of Group A.
But Berra believes the players should shoulder the responsibility for not snuffing out the threat of a Wales side who snatched victory thanks to a late double from Gareth Bale.
Asked if the players still back Levein, the Wolves defender said: "It's got nothing to do with the manager - we are the ones who go out on the pitch.
"We played well, we just maybe ran out of steam a bit. A penalty and a 25-yard strike lost us the game.
"At top-level football, it's the flip of a coin sometimes. We didn't have the luck.
"It's a game we should have won comfortably. Our chances came and maybe we should have killed them off."
Hopes of booking their place in Brazil appear to be all but over for Scotland, who now need victory over favourites Belgium on Tuesday to have any real hope of salvaging their campaign.
Berra knows the odds are stacked firmly against Levein's men ahead of Tuesday's clash in Brussels but he pointed out that Scotland have risen to the occasion in the past when written off.
He said: "We're second-bottom. It's not a great position to be in.
"But we will look over the game and we will go to Belgium on Monday and prepare for the game on Tuesday.
"They are a top team, with world-class players, but we have done it before. We did in France.
"When we're down, we always seem to bounce back.
"We didn't play badly against Wales. Lady Luck just didn't go our way.
"Footballers are thick-skinned. At club level as well, you get beat in one game, you've got to move on.
"We are disappointed now but you can't dwell on the past."
Scotland took the lead against the Welsh courtesy of a James Morrison first-half opener, before seeing what appeared to be a perfectly good Steven Fletcher goal disallowed with 15 minutes to go.
Bale then hauled the home side back into the match when he won and converted a penalty, before grabbing a superb winner in the final minute.
Berra said: "We don't know how we got beat, really.
"We played well in the first half, we passed the ball well and scored a route-one goal and had a couple of chances.
"They had more of the ball in the second half but they weren't cutting us open.
"It's a strange feeling. It was a comfortable game, we were winning 1-0. They had a lot of the ball in the second half but we weren't under much pressure. It's disappointing."
Berra admits the Scots should have dealt with the threat of star man Bale better late on.
He added: "He's a world-class player. I don't know if the first goal was a penalty or not.
"For the second goal, too many of us switched off and you can't give that kind of player 10, 15 yards to run into and have a pop at goal.
"On another day, he might have hit it over the bar. But he's got the ability and he put it into the top corner.
"It was bitterly disappointing for us. We should have won the game."
Berra paid tribute to the Tartan Army who travelled to Wales in their numbers only to leave the Cardiff City Stadium in stunned silence.
He said: "They were great, they backed us all the way. We are just as shell-shocked as them.
"We are disappointed we didn't win the game but the fans backed us 100% and we can only thank them for that."
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