Replays showed the Wales international was onside when he struck during Monday's 0-0 Premier League draw.
Rugby officials have access to instant replays of incidents during matches.
"To look at a video for 20 seconds would maybe have changed the outcome of the game," said Ramsey, 24.
He added: "We can take a leaf out of rugby's book. They do it really well.
"You see on the screens, they go up there for 20 seconds and they get the decision right in the end. Football can learn something from that."
Ramsey's effort would have given the Gunners an early lead at Emirates Stadium on Monday.
Television replays indicated he was in line with Liverpool defender Martin Skrtel when he collected Santi Cazorla's pass and finished past keeper Simon Mignolet.
Speaking after the game, Arsenal manager Arsene Wenger said assistant referee Simon Bennett had got the decision wrong.
It was the second time in two games the Reds have benefitted from a contentious offside decision.
On 17 August, what proved to be striker Christian Benteke's winner against Bournemouth at Anfield was wrongly allowed to stand despite team-mate Philippe Coutinho being in an offside position.
Football's lawmakers the International Football Association Board delayed trials of video technology for at least least 12 months at a meeting in February.
The Dutch FA had wanted to extend its trial of having a video official in the stadium watching replays and advising the referee on key decisions via a headset.
Fifa general secretary Jerome Valcke said at the time: "It's a question of making the biggest decision ever in the way football is played."
Arsenal midfielder Aaron Ramsey wants football to follow rugby's lead on video technology after he had a goal controversially disallowed for offside against Liverpool.