Windass, who agreed a move to Ibrox in January, failed to sign off his Stanley career in style.
The 22-year-old agreed a pre-contract with the Scottish championship winners in January, alongside Stanley teammate Matt Crooks.
The pair had been on course to end their Crown Ground careers on a high, with John Coleman's men occupying an automatic promotion place heading into the final weekend of League Two.
However, a 0-0 draw at home to Stevenage coupled with Bristol Rovers' injury time winner against Dagenham & Redbridge, saw Accrington drop into the play-offs.
And despite leading AFC Wimbledon 2-0 in the second leg of their semi-final encounter, Stanley squandered their advantage to draw 2-2 and miss out on a trip to Wembley 3-2 on aggregate.
Afterwards, Windass, who scored the opening goal of Wednesday's tie, tweeted his thanks to the club for giving him a chance when others weren't so keen.
And Rangers were quick to respond, quoting Windass' message and posting the words: "See you next season".
Rangers' season remains ongoing, with a Scottish Cup final date with Hibernian to come this weekend, however, their summer business is already underway.
As well as adding Windass and Crooks, the Light Blues have also brought in Liverpool's Jordan Rossiter and are in talks to sign ex-Premier League pair Joey Barton and Niko Kranjcar.