The 28-year-old winger put in a solid performance for the Reds as they sealed their passage to the Europa League group stages with a 2-1 aggregate win.
And the England international underlined his willingness to feature in defence should manager Brendan Rodgers choose to deploy him there again.
"I enjoyed the game," Downing told the club's official website.
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"I think you'll have to ask the manager whether I will play [in that position] again. Hopefully I'm in contention to play the coming games and if I start out wide or as a full-back, then so be it. I just want to play and do well and help the team."
The former Middlesbrough wideman went on to reveal Rodgers' commitment to winning Europe's second-tier competition and praised Hearts' performance at Anfield.
"We're in it to win it," he said. "As the manager says, this is a competition we want to win and I think you could see that by looking at the team selection tonight.
"A lot of people didn't think they would see the so-called big players but the fact that they did shows exactly what the manager thinks about this tournament.
"We made hard work of it but credit to Hearts, they came and had a go. We were a bit wasteful but thankfully, Luis grabbed the goal at a good time.
"It's good that we're in the groups but we'll carry on focusing on our league form for Sunday."