Benitez has been linked with a bid for central defender Turner, as well as Portsmouth's Sylvain Distin.
He also denied Sol Campbell's place at the club may be under threat to make way for Distin.
But Distin was sent off for upending Liedson inside the box and Veloso calmly slotted home an away goal.
Sylvain Distin's tap-in from a corner appeared to put the Toffees in control of the round of 32 first-leg tie.
Pompey boss Redknapp rang the changes at half-time bringing on Hermann Hreidarsson for Sylvain Distin and Arnold Mvuemba for Lauren.
City created the first decent opportunity after 14 minutes when Sylvain Distin threaded a pass into the path of Nicolas Anelka.
Distin inadvertently diverted a low cross to Marney and, symbolic of Everton's fortunes, the Hull midfielder's shot went in off Tim Cahill.
The equaliser came instantly, although Cahill was not involved, Distin's header from Arteta's free-kick sneaking past Hart, who should have done so much better.
Having hit the side-netting from Mulumbu's clever ball over the top moments earlier, Odemwingie reaped maximum advantage from Sylvain Distin's misreading of Brunt's lobbed pass.
And in Sol Campbell and Sylvan Distin, they were coming up against a resolute backline which was amply protected Diop, Sean Davis and Sulley Muntari.
There was more drama as Salisbury pointed to the spot with just two minutes of extra time remaining after City skipper Sylvain Distin had handled.
BBC: SPORT | Football | League Cup | Doncaster 1-1 Man City (aet)
However, the dreadlocked Zimbabwean finally registered on the scoresheet with 16 minutes remaining, beating Distin on the outside before firing low past a diving James.
Dunne has been linked with a move to Aston Villa, while Moyes is reportedly keen to bring Sylvain Distin from Portsmouth as a replacement for Lescott.
Sylvain Distin and Phil Jagielka marshalled Everton's defensive unit superbly throughout, pressing and closing City's forwards, while Johnny Heitinga was effective in breaking down the supply line.
The next significant Benfica attack was also initiated by Di Maria, and only a brilliant clearance from Sylvain Distin prevented Cardozo from doubling the home team's lead.
Adebayor was then denied twice inside three minutes - the first by a brilliant block from Sylvain Distin before Isaksson got down to keep out his powerful header.
Portsmouth, who have lost key players Peter Crouch, Jermain Defoe, Glen Johnson and Sylvain Distin this summer, made a bright start but City soon got into their stride.
And centre-back Nosworthy could come in as a replacement for Sylvain Distin, who was sold to Everton on Friday, if Portsmouth up an initial offer to meet Sunderland's valuation.
Saha had another effort saved before the moment which transformed the mood inside Goodison Park when substitute Jack Rodwell's overhit pass was miscontrolled by Distin, allowing Liedson to break clear.
The home side grabbed a controversial second shortly after the break when a Baines corner floated over a crowd of players to leave the unmarked Distin with a straightforward tap-in.
Everton were boosted before kick-off by the news that a deal had been agreed to sign Portsmouth defender Sylvain Distin, but it seemingly did little to rouse the starting XI.
And he has joined the trail set by Glen Johnson, Dimi Traore, Sean Davis, Peter Crouch, Sol Campbell, Sylvain Distin and now also Niko Kranjcar in leaving Pompey this summer.
Joseph Yobo's 10th-minute header was followed by a close-range finish by summer signing Distin from another corner seven minutes later, and a superb right-foot effort by Steven Pienaar on 37.
Just as the Brazilian-born striker shaped to shoot, he was brought down by Distin, leaving the referee no option but to give a penalty and show the Frenchman a red card.
Everton boss David Moyes, who fielded new signings Distin and Russia winger Diniyar Bilyaletdinov, later revealed the club have agreed a fee with Spanish side Atletico Madrid for defender Johnny Heitinga.
Hull went ahead after Everton defenders Sylvain Distin and Leighton Baines missed a deflected Hunt cross to allow Altidore to hammer a point-blank shot, which Howard did well to fend away.
Pompey manager Harry Redknapp had been linked with Distin a year ago when he was still under contract, so was delighted to see off reported late interest from Liverpool to get his man.
With Johnny Heitinga cup-tied and Sylvain Distin suspended, Everton had a new central defensive partnership in Yobo and Philippe Senderos - and the latter was very harshly penalised for a foul on Yannick Djalo.
The England striker appeared to have wasted the chance with a poor first touch but, with Sylvain Distin and James diving at his feet, he lifted the ball brilliantly into the back of the net.
Toffees centre-back Sylvain Distin could only loop a clearing header back towards his own goal to let in Cameron Jerome but the Blues striker controlled on his thigh only to half-volley wide from just inside the area.
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