The Reds are ninth in the table after a nine-match unbeaten run and O'Driscoll is not surprised that former Derby boss Davies is making an impact at the City Ground.
He told the club's official website: "They have big ambitions and for us to be playing in the same division as them is great.
"In Billy Davies, they have an experienced manager who knows what it takes to get out of this division. He's probably dug his heels in and said 'if you give me this, this and this; then I will make sure that you get where you want to get'. You admire him for that."
He added: "I think that last weekend against Middlesbrough, they probably had the strongest bench I have ever seen in this division. I can't remember a stronger bench - and you see those seven players who are not in the team and you realise why they are doing so well."