The 27-year-old winger scored just twice in 46 appearances in all competitions for the Reds since moving from Aston Villa to Liverpool in a £20m deal last summer.
Downing concedes his performances have not been good enough and vowed to improve his form under new Reds manager Brendan Rodgers in the next campaign.
“The goal thing is,” he said, when asked directly if his failure was embarrassing.
“The fact is I didn’t get enough goals. I hit the post and the bar many times and missed a few chances so I was disappointed especially when I scored goals for Aston Villa the year before.
“I try to score and maybe next season I will get 10 or 15.”
Downing, who has also been widely criticised for his lack of assists for frontmen Andy Carroll and Luis Suárez, staunchly defended his overall contribution to the team last term.
“Statistics have taken over the game: he doesn’t score this, he hasn’t set up that. You can read into it as you like,” he added.
“I’ve constantly set up chances, season in and season out.
“I can’t be criticised for not creating. I’ve just been unlucky that we’ve not finished the chances.”
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