Goals from Davide Faraoni and Lewis McGugan ensured the Golden Boys booked their place in the fourth round with a 2-0 win and after the game, Cotterill was full of praise for the home side.
"They’ve got some very, very good players here and I'm sure when they settle down they’ll start climbing up that Championship table," Cotterill said.
"They’ve got some very, very good players – very disciplined.
"Once they get their noses in front, there are quite a few Italian players who obviously have that mentality – they're very disciplined, very team orientated and they have some very good players."
Watford now face a trip in the fourth round to either Manchester City or Blackburn Rovers who play a replay at the Etihad tonight.
The Premier League outfit are strong favourites to go through and Cotterill admits the biggest disappointment is losing out on a potential tie against Manuel Pellegrini's team.
"Good luck to Watford, they're a good club," Cotterill said.
"Just the biggest disappointment really is we didn’t give our players potentially an opportunity to go to Manchester City which everybody would have thought about.
"There’s no point in hiding behind that - no disrespect to Blackburn - but our supporters and our players probably would have liked their day out up there but it wasn’t to be so we have to wish Watford good luck."