Rotherham manager Steve Evans was pleased with his side’s response after they came from behind to beat Crewe 2-1 and reach the second round of the Carabao Cup.
Matus Holicek gave Alexandra the lead in the second half when he latched onto a poor clearance from Alex MacDonald and curled beyond Cameron Dawson.
Rotherham levelled five minutes later with Sam Nombe heading in after Joe Powell had stood up an inviting cross.
Substitute Hakeem Odoffin secured the Millers’ passage to the next round as he turned in at the back post from Jonson Clarke-Harris’ header.
Rotherham were deserved winners and could have been out of sight at half-time with Clarke-Harris coming close twice and Jamie McCart and Sean Raggett missing from close range.
Evans was happy his side bounced back from an opening day League One loss to Exeter at the weekend.
The Scot said: “We are a work in progress but we need to win football matches. We can’t keep saying we are a work-in-progress because that is a cop out.
“I thought we showed a real hunger, desire and tenacity. I am pleased we have won the cup tie.”
Alex boss Lee Bell was left frustrated his side could not hold on for the draw which would have earned them a shot in the penalty shoot-out.
He said: “I thought we were excellent. We tried to play and probably overplayed first half. Ultimately, it’s a lack of concentration at the end that’s cost us.
“I thought we were good value to at least take it to penalties.”