The Birmingham midfielder dug his studs into Sagna's leg during Arsenal's 3-0 victory at St Andrews on Saturday.
He will now miss Tuesday's Barclays Premier League clash at Blackpool, the FA Cup Cup tie with Millwall on Saturday and next Tuesday's Carling Cup semi-final first leg at West Ham.
Trial by TV: Bowyer could face FA action for this alleged stamp on Sagna
Birmingham boss Alex McLeish said: 'We accept the decision and will now have to move forward into the next three games without the services of Bowyer.
'We have got a good discipline recordat this club and stress to the players every week how important discipline is.'
Referee Peter Walton told the FA thathad he seen the incident, he would have sent Bowyer off.
McLeish said on Monday that he would find it easierto stomach theprospect of aban forBowyer if he believedbigger PremierLeague clubs face thesame scrutiny.
McLeish highlighted whathe feels is an inadequate system ofretrospective trial by TV.
'As long as there is fairness, thereisn't a problem,' said theBirmingham manager yesterday.
'If things happen against our playersand we are tried by television,that has to be the same foreveryone.
Double standards: Alex McLeish says his side are being singled out
'I'll give you an example of whenit hasn't been. A month ago, nearthe end of the Spurs game, AlanHutton headbutted one of ourplayers, David Murphy, by thetouchline.
'I never said anythingabout it at the end of the game. Hutton came into the dressing-roomafterwards, apologised andshook Murphy's hand. But nothingwas done about it.
'However,on Match of the Day 2,the incident was shown. Thepundits were sitting on the sofasand they just laughed about it.They called Alan a 'little bull', andsuggested it was the way a bullwould butt somebody.
'I didn't see anyone screamingabout Alan Hutton that day. I wasquite happy to accept the apologyand let it be swept under thecarpet. I could have come out atthe time and asked, 'Why has henot been done?'
'But as soon as one of our playersis involved, then there is a bigfurore and Bowyer's got to be punished.I don't want to see peopletried by television. But if we aregoing to go through it, everyoneshould.'
The FA say Hutton's butt wasseen and dealt with at the time byreferee Kevin Friend when theteams drew 1-1 at St Andrew's onDecember 4.
Consistency: Birmingham boss McLeish says Hutton's clash with Murphy was just laughed off last month
Therefore,thedefender could not be subjected toany post-match action.But McLeish also suggested that,while Roger Johnson was criticisedfor a high tackle on Cesc Fabregasduring Arsenal's 3-0 victory, Gunnersmidfielder Samir Nasri camein for less scrutiny.
'Wewant fairness,' said McLeish.
'The challenge by Samir Nasri onStephen Carr at the end of the firsthalf was nasty. His studs wereshowing. If Stevie had stayed downthen it might have been different.But he is one of these guys whodoesn't like to show an opponentthat he's hurting.
'Nasri has just come in late. I'mnot saying it was a maliciouschallenge, but if you slow it down,you'll see Nasri's studs on Stevie'sankle. If that had been sloweddown, then you would have seenthat it was a bad tackle.
'Roger Johnson was booked forhis challenge. He miscontrolled theball and lunged after it. He wasbooked for that.
'With that one, thefollow-through was the damningthing. The day is going to comewhere players won't be able totackle.
'I don't know whether there'senough time in the day toscrutinise everything. We are lookingfor goalline technologyand there are so many things thatcould be done to improve thegame.
'But those are separate issues. Weare just after fairness. We are notdefending any player if they havemade a bad decision on the field.But it seems that the smaller clubsare always scrutinised. They needto look at the bigger clubsas well.'
An FA spokesman denied anypossibility of bias and insisted:'The FA apply retrospective actiononly to incidents that are deemedoff-the-ball and have clearly notbeen seen by the referee.
'The application of this is consistentto all incidents that are broughtto our attention.'
On hearing the news Bowyer had been suspended, Wenger said: 'Well the FA had a look at it and decided to charge him. I don't think I have any special comment to make on that. They judged him guilty and we have all to accept it.
'I think even Bowyer will accept that. He made a mistake, he has been punished and he will accept it.'
The Gunners boss rejected suggestions by McLeish they were one of the clubs who were not scrutinised as much.
He added: 'I just think the FA has to pick out any incident and punish every single club," Wenger said. I believe usually the media single out more the bigger clubs because they are more in the spotlight - but the FA has just to be objective and try to punish everybody no matter where he comes from. For every bad or violent player. If you want to sum it up I don't believe we have any favours from the media, no.'
'FA pick on the small clubs': McLeish rages as Bowyer faces trial by videoBowyer faces FA probe over vicious stamp on Arsenal defender SagnaAll the latest Birmingham news, features and opinion
Explore more:People: Alan Hutton, David Murphy, Roger Johnson, Lee Bowyer, Alex McLeish Places: Birmingham