Cowan had threatened a possible clear-out of his Bucks squad, who have under-performed so far this season, the latest defeat a 3-1 reverse at previously winless Blyth Spartans on Saturday.
And left-sided defender Morley, 32, has exited the New Bucks Head after just over a season with the club to rejoin former club and National North rivals Leamington.
Boss Cowan has a two-week break to make changes to his squad as the Bucks are not involved in the FA Cup this weekend following their exit against lower-league Nantwich.
"I just want people who want to be at the club," Cowan said. "Ultimately Steph has maybe orchestrated a move there because it suits his job and is closer to home.
"I want people who want to remain at the club and fight for the badge. If they don't want to then it doesn't matter how good a player they are.
"Form hasn't been overly brilliant for Steph. We obliged to let him move. We thought we could find better in that position and will hopefully make something happen this week."
The Telford chief is to look at options to boost his squad in replacement for any outgoing players.
Morley made 33 appearances for Telford – including eight this term – and scored four goals after joining in summer 2018.
"The players have got to work hard in every training session now when you do get a time like this. Like me as a manager, I've got to try to get it right and the players have to perform.
"It's fight or flight. In these situations you either lay down and die or stay positive. There's no delusion here, these are the same players that took us a long way in the league and cup last year and we have to remember they don't turn into bad players.
"Our philosophy doesn't become a poor one. We're just going through a tough time. The table will turn and everybody should belief it will happen soon."
Morley was shown a red card for a poor tackle in the recent Win Pryce Trophy fixture with Shifnal Town.
The defender was part of the majority of last season’s squad rewarded for their efforts by staying at Telford for another campaign.
Winger Chris Lait, midfielder Adam Walker and striker Aaron Williams were Cowan’s only summer recruits. Keeper Corey Addai checked in on loan from Coventry, but did not see out his month stint.
Attacker Lewis Reilly and defender Billy Sass-Davies have since joined on loan from Crewe.