Wayne Rooney admitted Birmingham City are in a 'difficult period' after suffering his eighth winless game in his nine matches in charge.
Birmingham were undone by former Aston Villa forward Callum O'Hare, who scored twice and for the first time since netting against the same opposition in a 4-2 win in April 2022.
Coventry fans taunted him with chants of 'Rooney', 'You're getting sacked in the morning' and 'Omne John Eustace' in reference to Rooney's predecessor and their former captain.
'It's disappointing and frustrating but we have to roll our sleeves up and dig in,' said Rooney.
'We're going through a difficult period and we have to stick together to pick up more points.
Callum O'Hare (centre) made a triumphant return to the scoresheet after unlucky ACL injury
Wayne Rooney has claimed just five points from a possible 27 since arriving at St Andrews
O'Hare was sidelined for seven months after picking up a knee injury on Boxing Day last year
Coventry City 2-0 Birmingham City: Match facts
Coventry City: Collins, Bidwell, Kitching, Thomas, Van Ewik, Allen, O'Hare, Sheaf, Wright, Simms, Sakamoto
Subs not used: Wilson, Binks, Latibeaudiere, McFadzean, Eccles, Dasilva, Kelly, Ayari, Palmer
Goals: O'Hare (30', 77')
Manager: Mark Robins
Birmingham City: Ruddy, Bacuna, Aiwu, Roberts, Buchanan, James, Bielik (Sunjic), Miyoshi (Burke), Stansfield (Hogan), Dembele, Jutkiewicz (Donovan)
Subs not used: Etheridge, Oakley, Khela, Longelo, Gardner
Booked: Bacuna, Dembele, Aiwu, Jutkiewicz, James
Manager: Wayne Rooney
'We have to keep trying to improve by working on the training pitch to try to get better results.
'We have to start picking up better results.'
O'Hare put the Sky Blus ahead on the half hour when he fired home after a one-two with Tatsuhiro Sakamoto.
The 25-year-old – making only his second start after 10 months out with a serious knee injury – capped a virtuoso performance with the second on 77, slaloming across the penalty area and beating Juninho Bacuna and Krystian Bielik before lashing home a rising shot.
'We conceded two sloppy goals – it's as simple as that,' moaned Rooney.
'I thought we started quite brightly but for the first goal, we allowed him (O'Hare) too much space in the penalty area.
'For the second goal, we've been working on defending the box and we didn't do it well enough.
'We've been working on playing more in the opposition's half and we had two or three shots when we need to keep the ball.'
Coventry boss Mark Robins praised O'Hare's contribution.
'Callum's a brilliant person – he's superb around the place, a really infectious character,' he said.
'He's worked really hard to get back to where he is at the moment and there's still more to come from him.
'He's got those touches, he loves playing football – I know he plays in the park with his old man.'
Haji Wright (left) had a number of strong chances, but was unable to get onto the scoresheet
Birmingham keeper John Ruddy was forced to work hard by a persistent Coventry City attack
Sky Blues fans called for Rooney to be 'sacked in the morning' after a triumphant home show
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