The former England midfielder moved back to the Riverside Stadium in 2015 - his second spell at the club - while Karanka left his post in March 2017 with the club heading towards relegation.
Downing, who has been in and out of the team this season, has since been told by new manager Garry Monk that 'he is not part of his plans' but is still determined to bow out on a high.
The 33-year-old told the Daily Star: "As soon as I walked through the door, it didn't feel right. I just didn't feel welcome.
"We were playing Stoke and [Karanka] put up the squad to travel but those who don't travel aren't told why. I asked why I wasn't in the squad and he said: 'I don't have to explain myself to you'.
"That wasn't the answer I was looking for. If he'd said I wasn't training well enough, then I'd have trained harder or whatever but this had rumbled on for months and months.
"The next thing I was getting booed, people thinking I got the manager out of the club but that's a load of rubbish. He left after an argument with another player, nothing to do with me. Everyone in Middlesbrough thinks it was me but it wasn't.
"Being booed wasn't nice but I wasn't allowed to say anything though I wanted to tell everyone what really went on and if you'd asked another 10 players they'd probably tell you the same thing."
Downing has made a total of 317 appearances for Boro during his two spells at the club.