Nyatanga was part of the Derby team which secured promotion via the play-offs in the 2006/07 campaign.
The Wales defender, who left the Rams to move to Ashton Gate in the summer, believes the Robins have enough strength in depth to secure at least a play-off place.
He said: "We have had setbacks with injuries and illnesses but we've got lots of good players here who can come in and do a good job.
"There is real competition for places and it's a long, hard season with a lot of games so it's vital to have a good squad."
He added: "The play-offs are a minimum target for us, we're looking to get into the Premier League and we don't want to get ahead of ourselves, but we set high standards."