Just gratitude and a growing suspicion that his own future might also lie away from Turf Moor.
Coyle will face the cries of Judas from those fans who have soon forgotten how he came south from St Johnstone to transform Burnley from a team in the lower reaches of the Championship to a Premier League club in 18 months.
They might accuse him of betrayal for joining a rival in the relegation battle, but Jensen is having none of it. 'Listen, he didn't really leave us in the s**t, did he?' said the big Danish goalkeeper known affectionately to Burnley fans as The Beast.
No grudges: Owen Coyle 'always had a smile on his face,' says keeper Brian Jensen
'We could have been at the bottom of the Championship with a horrible financial situation. He gave us £60million and if we stay in the Premier League now it's going to be even better.
'The fans don't really see the whole thing. They aren't looking beyond their frustrations. They want loyalty because they are loyal to the club. But they don't know what's going on behind the lines.
'See what we achieved. He got promotion to the Premier League in his first full season. I can't praise him enough for what has happened over the last couple of years.'
The speed of Coyle's departure and the cold snap which left many of his players snowed in meant they were unable to say goodbye in person, although the Scot phoned every one of the squad to let them know of his decision.
Pastures new: Coyle caused controversy by walking out on Burnley to join near neighbours Bolton
'The timing was bad but there are no grudges among the players,' added Jensen. 'We don't need to prove anything to Owen Coyle on Tuesday. He's the one who played us. We're there to play a football game against Bolton, not him.
'People need to look after themselves once in a while. If he felt it was what he needed to do for himself and his family then good luck to him.'
For the same reason Jensen, 34, is considering his own future. Burnley's longest-serving player is out of contract in the summer, and talks over a new deal have been put on hold while Coyle's successor Brian Laws settles into his new job.
Jensen said: 'They talked about a new deal before and the new manager has said, 'Listen, don't come knocking on my door straightaway, just let me get my feet on the ground and we'll come to you'.
'The timing is that I'm out of contract in the summer and I need to look after my family. The quicker we sort something out, the better.
'I've said all the way through that Burnley is where I feel I belong and where I want to stay. I've been here for seven years and I wouldn't change it if I didn't have to. But I'm open to suggestions.'
Jensen has been here before. He almost left Burnley three years ago, demanding to go on the transfer list after Coyle's predecessor Steve Cotterill signed Mike Pollitt on loan from Wigan.
'I just need to prove a point because I can't deal with people who don't tell you the truth and then do stuff behind your back,' he said. 'I'd rather someone came up to me and said, 'You are s**t'.'
There is no doubt Coyle brought the best out of Jensen. The Carling Cup heroics last season that helped knock out Chelsea and Arsenal; the penalty save from Michael Carrick that paved the way for Burnley's memorable victory over Manchester United in their first ever Premier League game at Turf Moor; and the performance at Stamford Bridge that prevented Chelsea's 3-0 win turning into double figures.
Not bad for a big lad from Norrebro in Copenhagen who started off as an outfield player but quickly took to goalkeeping when he went in nets at the age of 15 because he was 'the biggest and the stupidest'.
Jensen trained as an electrician, although he would rather have been a chef and still cooks every day for his wife Maria and their two sons Jamie, five, and Sebastian, three.
Now he is looking towards the end of his career, and the possibility of a move to America's Major League Soccer. He also wants to qualify as a goalkeeping coach but must first complete the UEFA 'A' licence.
Jensen admits he has struggled with a complicated course designed for outfield players. It makes him think of the simple things Coyle brought to Burnley every day.
'Everybody thought he was a magician,' says Jensen. 'Not at all. The main thing he did was to tell you that you were good enough. He gave us so much self-confidence and belief and that's 90 per cent of it in football.
'There wasn't a day when he didn't come in with a smile on his face. That was his philosophy: have good banter, crack jokes, work hard but, at the same time, enjoy yourself.
'What he was doing wasn't rocket science. It's basic stuff, really quite simple. He was just being human.'
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