Teale- who made three appearances whilst with The Reds in August played the full 90 minutes for the Rams at Old Trafford during their 4-2 defeat, whilst Welsh international Nyatanga - who made 53 appearances during three spells with Barnsley in 2006-2007 and 2007-2008 was an unused substitute.
Derby had won the first leg at Pride Park 1-0 where Nyatanga played the full 90 and Teale came on after 58 minutes.
Manchester United will now appear in their seventh League Cup Final against either the holders Tottenham or Championship side Burnley.
Meanwhile defender Rob Atkinson has completed his permanent move to League Two strugglers Grimsby Town