Brendan Rodgers' Swans held the Reds to their fourth home draw in just six games this season and added further doubt to their Champions League qualification credentials
Brendan Rodgers' men are the fourth visiting team to grab a point at Anfield this season in just six games, damaging Kenny Dalglish's side's chase for a Champions League spot.
Downing told the club's official website: "Swansea are a good footballing team and they've played well this season, but with no disrespect to them we need to be winning games like that at home if we want to get to where we want to be, so it was a bit disappointing for us not to get the three points."
He added: "It was disappointing to draw, but although Swansea played quite well, if we had put our chances away and scored early it might have been different.
"Probably the pleasing thing for the manager and the team is that we are creating chances. But we're not putting them away.
"We'll just have to keep working on it and keep getting ourselves in the right positions and hopefully they'll turn into goals soon."
The winger pointed to several key chances the Reds failed to finish and hailed the form of Swans goalkeeper Michel Vorm after he made two crucial late stops to keep the scores level.
He continued: "If Andy [Carroll] had scored with that early chance, it may have been a different game - Swansea might have had to change the way they played.
"It was a brilliant save from Glen's [Johnson] shot. I think the goalkeeper has probably been their best player this season, which shows how well he's done.
"But we had chances through Daniel [Agger], Glen as well as Andy's right at the start, and I'm not sure if Dirk's [Kuyt] goal was offside or not."