Liverpool's slim European hopes suffered another blow on Saturday after they were held to a goalless draw at Reading despite dominating proceedings at the Madejski Stadium.
The result means Liverpool trail sixth-placed Everton by five points and fifth-placed Tottenham Hotspur by eight, having played a game more than both sides.
Missing out on Europe would be a blow for Liverpool, but Downing believes they can push on next season after settling into life under Brendan Rodgers.
"This season was always going to be a transition time, with new ideas and players," Downing told the Daily Telegraph.
"Next season is a big test for us. He [Rodgers] has most of the players he wants and we have to crack on."
Downing insists they will not let their season fizzle out for the last five games despite qualification for Europe looking like a long shot.
"We won't let the season peter out," added Downing.
"The manager certainly won't let that happen. He has stressed that we keep going right to the end and see what happens.
"There are going to be slip-ups along the way but it's going to be tough for us, there's no hiding that. We have another big game coming up against Chelsea."
Downing admitted their failure to show more of a killer instinct when on top in games has been their downfall this season after failing to score from 26 attempts against Reading.
"Some of the chances we had, instead of making the keeper save them, we should have put them away," continued Downing
"That's been our downfall. The longer the game went on, Reading got more confident."