Osman replaced Diniyar Bilyaletdinov at half-time and gave Everton hope of a comeback when he netted a fine curling strike in the 57th minute. But Moyes’s men found it difficult to break down a stubborn Birmingham defence. “We should have ended up with a draw,” said the Goodison manager. “I can’t use that as a positive because our performance was so bad in the first half. I would have taken it though.

“It was disappointing. You don’t get many opportunities to win cups in this country, you are at home so you have to do better. That is all you can ask for.”

Moyes admits his side are suffering from a lack of killer instinct, and that as a result he would contemplate a temporary move for AC Milan striker Klass-Jan Huntelaar.

“I don’t talk about players at other clubs but if Huntelaar is available I would be interested,” he said. “I think we are lacking firepower at this time.

“We are creating a lot of chances but not finishing games off like I think we should.”

One player who will definitely be at Everton is centre-back Phillipe Senderos, who has arrived from Arsenal on loan until the end of the season.

The Switzerland international will come into contention for Wednesday’s Premier League visit of Sunderland, and explaining the move Moyes said: “We just needed another centre half. Joseph Yobo got a hamstring injury in Nigeria and Phil Jagielka isn’t back from his knee injury yet, I didn’t think I could go through this period with only two central defenders with Lucas Neill having gone. We have got him on loan until the end of the season. It gives me a bit of back up and cover.”

Meanwhile, Everton have agreed to sign goalkeeper Jan Mucha on a free transfer from Legia Warsaw at the end of the season.

The 27-year-old Slovakian international has penned a pre-contract agreement and negotiated a three-year deal with the Goodison outfit.