Coyle's timely exit meant that he avoided questioning over his commitment to Burnley as speculation continues to link him with the vacancy at neighbours and Premier League rivals Bolton.
Stewart admitted that he hoped to continue to be Coyle's assistant at either club, but did have some good news for Clarets fans when he confirmed that talks were ongoing over bringing Wilshere to Turf Moor.
Wilshere - who was 18 on New Year's Day - has caught the eye for Arsene Wenger's side and would undoubtedly bed in to Burnley's fluid attacking style.
Stewart said: "Owen and I have a great partnership. We have worked together at St Johnstone and Burnley so, whatever happens, hopefully that partnership will continue.
"At this moment in time, that will be at Burnley.
"As of yet there is no progress on Jack Wilshere.
"He is a player we have earmarked as one who would do very well for Burnley. We like his style of football and believe that he would blend into our system well.
"He is one we definitely like and there has been dialogue between ourselves and Arsenal but as I understand it there are a couple of other interested parties so we will just have to wait and see."
Stewart also revealed that talks to allow on-loan Portsmouth striker David Nugent to face Paul Ince's League One side had continued right up to kick-off.
Pompey eventually refused to allow the former Preston man to play and leave Coyle and Stewart frustrated.
Stewart said: "David has become an integral part of the squad and has done very well for us.
"We had hoped for him to play but unfortunately Portsmouth wouldn't give us permission so there was nothing that could be done.
"The negotiations went right to the last minute as we were desperate to have him available but it wasn't to be and it allowed someone else an opportunity to impress."
Ince was pleased with his side's performance and revealed that the intensity of the second-half fightback may have changed his plans for the January transfer window.
Goals from Graham Alexander and Steven Fletcher had put the Clarets in control but Ince's side mounted a fierce late surge that culminated in a goal from Dean Morgan
Ince said: "We are taking baby steps and the last few performances have been outstanding.
"I can go back and think the future is bright.
"I wanted to get five or six in this month but after that performance I may change my mind.
"I am not in a position where I can spend a lot of money but I will sit down with the chairman and hopefully get two or three in.
"If they keep playing like that though it will make my job easier."