With one match of the regular season left to play, Wrexham sit above seventh-placed Hull City on goal difference and a point clear of Derby County who are eighth.
It is a scenario boss Parkinson says his side would have taken “all day long”.
And Ollie Rathbone – who netted his eighth goal of the campaign across all competitions in the loss at Coventry – says his side’s disappointment at losing to Frank Lampard’s champions typifies the improvement Wrexham have made over the course of the second tier season.
“At the start of the season, everyone would have taken this scenario,” said Rathbone.
“It shows how much the team has evolved that we’ve come to the best team in the division and we’re disappointed that we’ve not taken anything away.
“I’m hugely proud of that growth, but ultimately it’s disappointing today.”