Top-six finish is still Saints' minimum target
The black, green and gold currently sit 10th in the league standings, having won just five of their 14 matches to date.
Their most recent setback came at The Rec last weekend, with Bath securing a comfortable 32-9 success.
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Hide AdSaints struggled to find a spark and they now sit 11 points behind sixth-placed Sale Sharks and 16 adrift of fourth-placed Gloucester.
But technical coaching consultant Gaffney is determined to keep looking up.
"We're not going to aim for bottom three or four so we're still going to aim for top four, top six," the Australian said.
"We want to be top six at worst and what happens after that is a bonus.
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Hide Ad"There's always an aim to get into Europe and play against the better sides next year with (new boss) Chris (Boyd) coming in for next season.
"Hopefully we can lay a platform for them to perform well in all competitions.
"We'll still set our sights where we had them."
Saints host bottom side London Irish on Saturday.
Gaffney's men are 15 points ahead of Irish in the league standings and will look to push further clear of the relegation place this weekend.
"We've got to start again this week and go in against Irish," Gaffney said.
"It's a critical game as far as we're concerned.
"We're not looking at it as a relegation battle, we're looking up the table, not down the table.
"We've got to go and put a good performance on at Franklin's Gardens for our supporters."