The former Aston Villa player was the subject of criticism after failing to score a single Premier League goal in his first campaign with the Merseyside club.
"I was disappointed with how last season went but I'm not sure I'm a 'confidence' player," Downing told the Liverpool Echo.
"I just like to be in the team and doing well. It's not nice when you are not getting results and we certainly took a lot of stick last season when it wasn't happening, especially with us new players coming in."
The Reds will begin the new season with an away trip to West Bromwich Albion on August 18.