Stephen Ireland's 67th-minute volley, after good work by substitute Darius Vassell, was enough to hand City a win which lifts them to third.
Coming after last week's 6-0 hammering at Chelsea, Dunne told Setanta 1: "The manager has not set any targets.
"We are enjoying it at the moment and if we keep working hard we'll be in the top half, and hopefully challenge for the European places."
He added: "We needed to bounce back after the defeat so it was nice to get the win.
"It's been good. We were very disappointed last week and we know if we are strong at the back we have the quality up front to score goals."
City manager Sven-Goran Eriksson saw his side set a new club record of seven straight home wins - but admitted it had not been a pretty game.
“We took the three points and we are all very happy with that,” he added.
“It was not a great game, Sunderland played well and made it difficult for us, we missed a lot of passes and didn’t play the football we can.
“It’s very important for us after playing Chelsea away that we won and had a clean sheet. The good football will hopefully come again soon.”
Of the goal-scorer he added: “Stephen Ireland is a fantastic football player. Especially in the second half he played very well.”
Do you think City can maintain their lofty league position? Have your say.
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Ooh Vonky Vonky.., Offerton (05/11/2007 at 22:25)
Least we are winning whilst were not playing well. Just need to keep winning at home and try and improve away form then fill the gaps in Jan transfer window.
Pompey will be a test of character after our last away day, just hope we can get ack to the slick football we played against the barcodes and Boro.
CTID