Defeat at the Checkatrade.com stadium ended Crawley’s three-year stay in League One, and there is also uncertainty over who will be in charge of them next season with Dean Saunders having taken over from John Gregory on an interim basis.
Crawley were given hope of beating the drop when striker Mathias Pogba headed them ahead just after the interval, but late goals from Marcus Tudgay and substitute James Maddison settled the issue.
Coventry went into the game only needing a point to be certain of staying up, and Mowbray admitted it would have been a “long way back” had the worse happened and they had been relegated.
He said: “Hopefully I’ll be here next season but some things will have to change. Coventry are in the wrong league and rebuilding and restructuring need to begin now.
“The club deserves to be higher and we must aim to get out of this league as soon as possible.
“There will be conversations in the middle of the week and I’ll speak to the owners.
“As a fresh pair of eyes coming into the club I’ve seem some things I like, but some things regarding the infrastructure can be improved.”
Mowbray, who took over at the start of March, insisted there was no real cause for celebration, although he was delighted that City signed off with a win before 1,600 travelling fans.
He added: “There is a long way back from League Two as Portsmouth have showed. There is no celebration at staying in this league; the goal is to move into the Championship as soon as possible.”
Saunders described the feeling of relegation as “sickening” coming as it did after his side’s failure to win one of their last two games to clinch survival.
The Welshman felt losing at home was another “slap in the face” coming hard on the heels of the damaging 4-3 defeat at Peterborough the week before.
He admitted: “Losing at Peterborough was the biggest slap in the face I’ve ever had so this is sickening really.
“We got ourselves in a position where we needed one win from our last two games but we haven’t got over the line.
“I’m absolutely gutted that we haven’t done it, but losing Richard Wood and Anthony Wordsworth has cost us.
“Wood’s recall to Rotherham desimated our defence and I’ve had to patch it up at the wrong time of the season.”
Saunders revealed he will be speaking to the club on Tuesday regarding the future having taken charge just after Christmas from former Aston Villa boss Gregory, who stepped down due to medical reasons.