Saints beat Norwich City (who are Blades opponents next week) 2-0 to get into the last eight, though it was not a convincing performance from the St Mary's faithful.
The red haired manager was in a good mood after the game (you would be too if your team had won) but admits that he would prefer to avoid Neil Warnock's Red and White Wizards in the next round.
Strachan said: "I remember with Coventry when I was manager there a few years ago we had knocked out some top sides but then lost on penalties after a replay against Sheffield United. I don't think we scored even one of our penalties.
"But when you get to the quarter-finals it is no good fearing anybody. With Manchester United and Sunderland losing, that is two more Premiership teams out which makes things easier - but I fancy our chances against anybody with this side."