With Premier League leaders Liverpool playing in FIFA’s Club World Cup 24 hours later in Doha, Villa faced an unrecognisable line-up featuring no senior players.
Liverpool’s starting side had only 16 first-team appearances between them and had an average age of 19.4, a club record.
Villa themselves made 10 changes from the side that lost to Sheffield United in the Premier League on Saturday, but were still put in a “no-win” situation against the Anfield kids on a strange night at rainy Villa Park.
“We had to be very professional,” Smith, who has taken Villa to their first League Cup semi-final since 2012-13, said.
“It was a bit of a weird game, probably the weirdest one I’ve been involved in for a quarter-final of a major competition.
“They had technically gifted players, were tactically switched on and they made it very difficult for us at times.”
Villa’s Conor Hourihane, whose cross opened the scoring in the 14th minute after a nervy start by the hosts, said it had been a tricky test against players with nothing to lose.
“We weathered the storm at the start but quality came through in the end,” he said.
“It was lose-lose but we did a professional job and we are delighted to get over the line. Nice to get through to the semi-finals. That is what we had to do tonight.”
Liverpool’s under-23 manager Neil Critchley said he was proud of his players. He was standing in for Jurgen Klopp, who phoned him at half-time from the team’s Doha hotel.
“It was an incredible night and no-one wanted it to end. The support we had was unbelievable,” he said.
“The conduct of the Villa players was first class. For Dean Smith and (assistant manager) John Terry to come in to our dressing room after the game and say the things they said... They said ‘keep going, good luck’ and wished us the best - a moment I will remember and the players will remember for the rest of their lives.”