Steve Boden’s men prevailed 31-27 on Sunday but that was not enough to overturn the first leg deficit and the hosts won 62-53 on aggregate.
In a fiercely contested match, Knights fought relentlessly to go through and scored three excellent tries in the first half.
Winger Kyle Evans went over on five minutes following a break by full-back Harry Davey and Maliq Holden scored in the 14th minute following a thrilling attack involving fly half Sam Olver, centre Fraser Strachan and Davey.
John Kelly also charged over on 34 minutes, capitalising on work by his pack.
Throughout the second half both teams were neck and neck and suffered yellow cards.
Coventry started the stronger, scoring a converted try, their third, plus a penalty from fly half Tony Fenner.
But, earlier on 61 minutes, Doncaster’s chances were boosted when they were awarded a penalty try, providing a 31-24 lead which slashed Coventry’s advantage to six points only.
An exciting cup tie effectively ended in Coventry’s favour in the 75th minute with Jenner’s second penalty stretching his team’s lead to nine points and earning them a place in the semi-finals.
However, Doncaster, who have enjoyed a memorable but tiring season, should not be too disappointed and can look forward to a decent summer break.
Coventry: Brown, Aspland-Robinson, James, Forsyth, Martin, Fenner, Babos, Trinder, Poole, Andrews, Tyas, Peters, Betteridge, Bainbridge, Nayalo.
Doncaster: Davey, Evans, Edwards (Margetts 64), Strachan, Holden, Olver, Dolly (Green 64), Davidson, Roberts, Ford, Kelly, Murphy, Hudson, Graham (Volpi 59), Smith.
Referee: Hamish Grant (RFU)