Slow-starting Sunderland eye League Cup fillip
Sunderland manager Dick Advocaat found himself in the spotlight after his team lost their opening two league games, but they stopped the rot by recovering from a goal down to draw 1-1 at home to Swansea City on Saturday.
While Sunderland failed to win, it was a much-improved display and O'Shea is hopeful that it will prove a turning point.
"We've Exeter now and we'd look to win that and move on into the next round of the cup," the former Manchester United defender told the Sunderland website.
"Whoever you're playing against in the cup, if you have a home draw you want to get the win and move on."
He added: "The negative vibe around because of such poor performances has not totally gone -- we didn't win, we got a draw -- but it's something to start with."
Sunderland's next league outing is at Aston Villa next weekend and Tim Sherwood's side are also in need of a pick-me-up ahead of their encounter with Notts County of fourth-tier League Two.
Having won at Bournemouth on the Premier League's opening day, last season's FA Cup finalists subsequently lost to Manchester United and Crystal Palace.
- Stones's Barnsley reunion -
But having seen his side work their way back into Saturday's game at Palace, only to go down 2-1 to an 87th-minute Bakary Sako goal, centre-back Ciaran Clark says Villa can draw encouragement from their latest display.
"We did really well to pull it back and with a couple of minutes to go it was just one of those things," he told the club website.
"We'll learn from that and we'll move on to the next game. That's all we can do."
Leicester City, flying high in the Premier League after three unbeaten games,Â visit third-tier Bury, while Newcastle United host Northampton Town and 2013 winners Swansea, also unbeaten in the league, face York City.
Second-tier Milton Keynes Dons, who created a sensation at this stage of last season's tournament by humiliating Manchester United 4-0, entertain fellow Championship representatives Cardiff City.
United will enter the competition in the third round along with the seven other Premier League teams competing in Europe, including Arsenal, Liverpool, Manchester City and holders Chelsea, who beat Tottenham Hotspur in last season's final.
The third-round draw will be made after Everton's home game with Barnsley on Wednesday, when the Merseyside club's centre-back John Stones, strongly linked with a move to Chelsea, will line up against his former club.