After netting the Reds' only goal in their first-leg victory over FC Gomel in the Europa League third qualifying round, the winger is looking for them to build and get better
The Reds went into the first leg just a few weeks into their pre-season preparations and the winger believes that his side will be improved after another full week of training.
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He told the Liverpool Echo: "I think we were all a little bit rusty. It was my first 90 minutes and Johnno [Glen Johnson] came back in after playing all summer and Gomel are five or six weeks, if not longer, into their league season.
"I can understand fans who want us to be fast out of the blocks but we had only been back 10 days so for me it was a good result, maybe not the best performance but with a week's training behind us we'll put a better performance in at Anfield tomorrow [Thursday] night."
Downing notched the only goal of the game in Belarus, and after a goalless Premier League campaign last term, the former Middlesbrough man revealed Brendan Rodgers is looking to utilise him on the right wing in an attempt to create more goalscoring opportunities.
He added: "I was really pleased with the goal. It was good timing as well because we were under pressure a little bit and it deflated them a little.
"All managers have their different ways of playing and this manager sees me as playing on the right a little bit more.
"He wants me playing higher up the field and getting in goal scoring positions because maybe I was a little bit deep last season. Hopefully that will happen and I will be in the position to score more goals."
Despite many teams often viewing the Europa League unfavourably and choosing to play largely reserve squads in the competition, Downing insists that Liverpool are eyeing success in the competition this season.
He said: "It's certainly one we want to win.
"Earlier on you don't know where you are going to be playing but the further on you get, when the Champions League teams drop in, then there are some good sides in the competition.
"The manager has stressed from day one that whatever competition we are in, we go to win it. So you can see his mentality, he wants to win every game, he is hungry and his players have got to be the same otherwise you don't get picked."