Smith’s powerful effort in the dying minutes at Villa Park saw City through to the semi-final after Jadon Sancho had equalised early in the match.
The Welsh midfielder’s goal was the first time City had been ahead in the tie, despite testing Villa goalkeeper Viktor Johansson on a number of occasions, and Carsley was impressed with his team’s attitude.
He said: “When you look at the amount of chances that we created, the amount the ball has whizzed across the box from the first minute to the last minute, you see we were the better team.
“Their plan was to frustrate in a similar way to Liverpool and Southampton and we found it difficult to break them down.
“If we had got in the lead early they would have had to come at us a little more but it wasn’t to be so we had to find a way through a packed defence.
“It potentially could have been a sticky night because their goal was from a scrappy set-piece and then you can end up losing that game 2-1 from a counter-attack.
“It was a relief when Matty scored in front of what felt like his home end given all of his family members in the stand!”
City will face Preston or Stoke in the semi-final but Carsley believes City’s experience of playing at Villa Park will stand them in good stead for the future.
He said: “You’ve got to remember that we’ve come to Aston Villa, who are a top academy, and we’re playing under the lights at Villa Park.
“All that brings a new experience and we’ve had some really good sessions in the lead up to the match.
“The further we go in the competition I think the more there is come from this group. It’s easier to pick teams off when they come to attack you but we’ll have to find different ways of beating teams.”
Having made several changes from the victory over Southampton, the former Ireland international praised the depth and flexibility of his squad.
“We’ve got that many players at a high standard and hopefully we’ll have them all to choose from in the next round.
“I think it [my strongest team] has varied. If you asked me from [the pre-season trip] to Croatia to now, it would be totally different. You have to take in to account who is in form, who isn’t and who needs a rest to make sure that on the night they’re all ready for it.”
Keep up to date with all the latest on the EDS and academy on Twitter at @ManCityAcademy.
