Downing almost scored within three minutes of being introduced but was denied by a fingertip save from substitute stopper Adriano Basso.
Afterwards he told liverpoolfc.tv: "It could have been a dream debut. I thought it was in to be honest but it was a great save from the 'keeper.
"We created a lot of chances but just didn't put them away - hopefully we're saving that for the season.
"It's been good training, I've enjoyed it up to now and it was nice to be out there. A disappointing result but pre-season is all about fitness."
Downing completed his move from Villa Park nine days ago and claims he is enjoying his new life in the north-west.
"It's brilliant so far," he said. "It's a top football club and I'm getting looked after very well! Hopefully I can make an impact and do my best.
"I did a week at Aston Villa and a week here so I just want to get out there, get underway, get the debuts out of the way."