Middlesbrough's 1-0 defeat to Portsmouth meant Frank Lampard's men would have secured promotion had they beaten the Owls.
But the enormity of the occasion appeared to get to Coventry as they fired a rare blank at home this season.
"We normally score here, we normally win games here, so we have to keep a bit of perspective," said Lampard.
"I know there's a pressure and everyone wants to release the pressure by getting it done and now we have to move onto the next one."
It remains a matter of when, not if, the Sky Blues will secure Premier League status as they moved 12 points clear of third-placed Millwall with four games remaining and have a vastly superior goal difference.
Ipswich took a massive step towards joining Coventry in the top flight next season with a 2-0 win at local rivals Norwich.
First-half goals from Jaden Philogene and George Hirst completed a first league double over their East Anglian neighbours for 33 years.
Kieran McKenna's men moved two points ahead of Millwall and have two games in hand in the battle for automatic promotion.
Middlesbrough's challenge for a top-two finish has come off the rails at the business end of the campaign as they are now six games without a win.
Andre Dozzell's deflected effort seven minutes into stoppage time gave Pompey's bid for survival a huge boost.
Portsmouth's victory also plunged Leicester ever closer to the third tier, just a decade on from winning the Premier League.
The Foxes lost their appeal against a six-point deduction for breaching financial rules this week.
A 1-0 home defeat to Swansea leaves them second from bottom and four points adrift of safety.
Southampton's stunning form continued as they came from behind for a 2-1 win over Derby to solidify their place in the play-off places.
Leo Scienza and Taylor Harwood-Bellis struck for the FA Cup semi-finalists as Southampton extended their unbeaten run to 17 games.
Hull's play-off hopes were dented by a 2-1 defeat at Sheffield United, dropping them to sixth.
Oxford beat Watford 2-0 to remain just one point adrift of safety.