The ex-Wolfsburg goal-scorer made his Turf Moor switch for £12m at the end of the winter transfer window, but scored only twice in 20 appearances as the Clarets returned to the Championship.
However, with many fans displeased with his conduct, Weghorst insists that his words were lost in translation. He said: "I'm really thankful for last year, that's something I wanted to say to the fans.
"There were some tough weeks after the relegation and for me to get everything straight after I played for the national team. I had an interview over there — it was translated so I don't know if it was an English one or a Dutch one — but it wasn't totally right.
"You know how the media can work sometimes. It was really important for me to speak to the fans and the club."
The Borne-born finisher accepted that the intention had been to move on after Burnley were dumped from the top flight — an agreement that had already been put in place on his arrival at the club.
That decision, he says, wasn't one made out of disrespect or arrogance. Weghorst feels it was necessary if he was to have any chance of making Louis van Gaal's squad for the World Cup in Qatar in November.
He said: "I had my thoughts about it, I had my thoughts about it before I moved to Burnley half-a-year ago. The World Cup is coming up now and that's a really important thing for me.
"It's my biggest dream, I think it's the highest you can achieve as a professional football player. We have a trainer who has clear thoughts on playing at the highest level so he's really strict about it. If I wanted to be there I had to make a decision.
"It's not that I feel too good for the Championship or that I don't want to play in the Championship with Burnley, because there are reasons for it from my side. I spoke about it with the club before I came."
Sources in Turkey suggest that the 16-time champions, who relinquished their crown last term, have an option to buy the striker next summer for somewhere between €10-14m.
But Weghorst isn't ruling out a return: "I think the connection was there and I felt it at the beginning. They [the fans] were the main reason why I wanted to sit down and speak and be open and honest.
"The Burnley fans at Turf Moor made the whole Premier League dream I had in England. They made it special, they're beautiful, the songs they sung for me, it'll always be something I'll keep in my mind. They will always have a place in my heart.
"I hope there could be a return from my side and we could have more positive and successful moments together. I'm looking forward to that moment."