With Gael Clichy also out, Armand Traore could deputise at left-back when Arsenal host Chelsea on Sunday.
Walcott made it 2-1 with a mazy run and shot before McFadden equalised after Gael Clichy fouled Stuart Parnaby.
He raced forward and found Drogba, who swept past Gael Clichy with embarrassing ease before powering a shot beyond Manuel Almunia.
Deep into injury time, Bent pounced to smash in from inside the six-yard area after Gael Clichy had failed to clear.
Nasri will join a large French contingent at Arsenal which already include captain William Gallas, Gael Clichy, Abou Diaby and Bacary Sagna.
At the other end a fantastic blocked clearance by Gael Clichy denied Sheringham the chance to grab his second goal in a week.
Gael Clichy's cross was headed off target by Nicklas Bendtner, who then failed to get on the end of another dangerous ball from Nasri.
Substitute Gael Clichy then lashed in low with 15 minutes remaining.
Arsenal are also currently without the injured Gael Clichy and Denilson.
Arsenal also lost Russia forward Andrei Arshavin and France defender William Gallas to calf injuries, while Brazil midfielder Denilson and defender Gael Clichy are also doubtful.
Gael Clichy crossed from the left for Van Persie to head against the crossbar and Baggies goalkeeper Scott Carson spread himself well to repel Ramsey's close-range follow-up.
Ferguson's selection of Tevez ahead of Dimitar Berbatov suggested he wanted an energetic, high-tempo approach against an Arsenal defence undermined by injuries to influential pair William Gallas and Gael Clichy.
Bendtner should have equalised for Arsenal after 53 minutes when he arrived on the end of Gael Clichy's cross, but his header from eight yards was brilliantly turned away by Valdes.
The Baggies had still to find any sort of rhythm when they were cut apart by a smooth interchange of passes involving Bendtner, Gael Clichy and Denilson that led to Nasri's opener.
Then, Arsenal all but booked their passage into the next round in the 71st minute when Caldwell diverted the ball past Boruc in his attempt to cut out a Gael Clichy left-wing cross.
United could have enjoyed a more comfortable victory had Wayne Rooney not fired his penalty high and wide of the Arsenal goal, after the Gunners full-back Gael Clichy was deemed to have illegally handled.
BBC: Arsene Wenger blames Man Utd pitch for Arsenal mistakes
After turning Gael Clichy inside out, Varela crossed a relatively harmless ball in from the right, only for the Polish keeper, in for the injured Manuel Almunia, to spill the ball into the net.
Sean Davis had the first shot of the match, and went close with a curling effort before Djimi Traore hooked the ball off the line at the other end when Gael Clichy's cross took a deflection.
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Emerton was at the heart of most of Blackburn's best attacking play, and the Australian carved out another chance when he beat Gael Clichy on the right, only for his cross to just evade Keith Andrews' driving run.
Cole's dismissal had come shortly after a Glen Johnson shot had been tipped over the bar by Arsenal keeper Manuel Almunia and an Ngog header from a Gerrard corner had been cleared off the line by Gael Clichy.
Arsenal's midweek match-winner Eduardo was the central figure in the third goal, striking a post with a volley from a Gael Clichy cross before driving in a follow-up effort which found the net courtesy of a telling deflection off Eboue.
The Gunners, who face Olympiacos in their final Champions League group game in Athens on Wednesday, are already without Robin van Persie (ankle), Nicklas Bendtner (groin), Gael Clichy (back), Theo Walcott (hamstring), Abou Diaby (calf), Kieran Gibbs (ankle) and Johan Djourou (knee).
Wenger made four alterations to his starting line-up - Eboue, Kieran Gibbs, Diaby and Eduardo replacing Bacary Sagna, Gael Clichy, Alexandre Song and Nicklas Bendtner - but the change of personnel did little to disrupt a rhythm that had brought Arsenal impressive wins against Everton and Celtic.
BBC: SPORT | Football | Premier League | Arsenal 4-1 Portsmouth
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