There was a change at half-time with Emily Orman replacing an injured Chloe Morgan, who picked up a strain in the first-half.
Just minutes into the second-half Coventry were through on goal. Grace Coombs fouled the away striker which resulted in her being shown a straight red card, leaving the Eagles down to 10.
Coventry’s Mollie Green stepped up to take the resulting free kick but it was blocked by Palace's wall.
Despite being down to 10 the hosts continued to challenge Coventry. Sharpe was gifted the ball just inside the area and crossed it into the box, but her effort sailed past those in red and blue.
New signing Hennessy made an excellent run towards the box, but was unable to get a shot on goal as she was blocked by the away defence.
So it was Coventry who broke the deadlock in the 67th-minute, with a cross from Olivia Fergusson met by Katie Wilkinson and headed past Orman.
The Eagles continued to look for an equaliser, and deep into stoppage time were awarded a corner which Shiv Wilson delivered into the box, but it proved to be the final unsuccessul chance of a harsh game.
Next up Palace travel to Lewes to face them in the Women’s Championship.
Crystal Palace: Morgan (Orman 45), Johnson, Coombs (Red card), Pearse, Clifford (Barton 12), Sibley, Cowan (Farrow 78), Everett, McLean (68 Wilson), Sharpe, Hennessy (68 Churchill).
Subs not used: Baptiste, Nicol, Haines, Waldie.
Coventry United: Thomas (Colville 90), N’Dow, Wilcox (Fergusson 19), Green, Morris, Orthodoxou, Johnson, Estcourt, Thomas, Mann, Wilkinson.
Subs not used: Clark, Hartley, Riglar, McGrother.