The Bluebirds head into the Cardiff City Stadium clash against Crystal Palace looking to hit back following their 1-0 defeat at Selhurst Park a fortnight ago.
A repeat of the 2-0 home win Cardiff enjoyed in the Championship meeting between the sides would be enough to send the Welsh club through to their first League Cup final, and a third Wembley appearance in five seasons after defeats in the 2008 FA Cup final and the 2010 play-off final.
And Scotland international Miller wants his team-mates to show the same patience which secured the three points back in November.
He said: "This will be the third time we've played them in a matter of weeks and we know the way they want to play.
"It took us until around the 70th minute to make the breakthrough in the league game so we know what the game will bring. We have to be patient.
"If we get an early goal then great and it can lead to an exciting night but if it's still 0-0 at half time we still have another half to win it and we are more than capable of doing that.
"Many times this season we have been 0-0 at half-time and come out and got the win in the second half.
"Patience will be the key word, they will play how they play, they can hit you on counter so we know we will have to keep an eye open for that, but we don't want to get rushed into it and start throwing things forward to get a goal. We just need to play how we play and hopefully the breakthrough will come.
"We know we have enough in the locker to beat them by the required number of goals."
Miller also insists the Cardiff squad have paid no attention to comments made by Palace boss Dougie Freedman in which he said the Welsh club would be "scared stiff" of losing out in another big game following their play-off anguish over the last two seasons.
Miller said: "I haven't seen it, the manager mentioned it but I don't think we will be scared stiff.
"It's a chance for us to put right the result we did not get in the first leg. Mind games come into it when you are a manager but it means nothing. We are just going to play a game of football and try and get a result."
Darren Ambrose scored a cracker at Old Trafford to send Palace into the last four but he is warning against playing for a clean sheet - something which would see them reach Wembley.
Ambrose said: "If we go into the match with that attitude then we will get turned over.
"We played Cardiff two months ago and lost 2-0 and and if it is the same score they'll be through.
"We have to go in with the attitude that it is 0-0 and we need a goal. If we can score once then they will have to score at least three times over 120 minutes.
"If you can't enjoy games like this then you shouldn't be playing football. These are the games you dream of when you are growing up. Big nights like this in the semi-finals.
"We're not nervous at all. We are 90 minutes away from a big cup final but I think if everyone can go out there and enjoy themselves we'll be all right."