Rotherham United: A case of what might have been for Warne in Everton defeat
The Millers, who lost League Cup ties at Goodison Park in 1987 and 1992, competed well against a strong Toffees side, but went down to Dominic Calvert-Lewin's brace after a Gylfi Sigurdsson opener.
Will Vaulks had briefly got Warne's men back in it with a late header, but they never really had enough to threaten an upset '“ though left Merseyside with their pride in tact.
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Hide AdWarne said: 'We started the game pretty well. I was hugely disappointed with the goals we conceded but I am not disappointed with the effort the lads gave me.
'At 2-1 I honestly believed we were right in it, overall I am proud of the lads but disappointed that it could have been a little bit better.
'There is a lot of pride to take out the game. I think the lads gave a good account of themselves.
'On another day it might have gone another way.'
Warne had to make a late change to his team when Joe Mattock, who was carrying a knock, pulled up in the pre-match warm-up.
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Hide AdThe left-back, who watched central defender Clark Robertson play in his position, is now a doubt for Saturday's Championship trip to Wigan.
Warne added: 'He's a doubt on two-folds, one that Robbo did really well and two that he is sore and the next game is coming very quick, and I like the players who are going to play to train.
'So that makes him a massive doubt.'