Aspas netted the opening goal of the game with a volley in front of the Kop as Liverpool progressed to the fourth round of the competition with a 2-0 win over the League 1 side.
And Toure believes Aspas' strike will give him some much-needed confidence as Liverpool try and secure qualification for the UEFA Champions League for the first time since 2009.
"This goal will change him, definitely," the Ivory Coast international said.
"It's very important for a striker to score goals. Their confidence comes from scoring goals.
"The Premier League is a tough league - it is the best league in the world - and he is a young striker who was fantastic for Celta Vigo.
"We know what he can do. He just needs time. He hasn't played many games since he came here but he scored a great goal for us.
"He did really well and we are all really happy for him."
Winger Raheem Sterling, who supplied the assist for Aspas' goal, echoed Toure's sentiments, adding he was pleased to see the Spaniard reaping the dividends of the hard work he puts in on the training ground.
"It will give him a big boost," the 19-year-old said. "He comes in and every day in training he's scoring goals and creating chances.
"Sunday was a great opportunity for him and he scored, so hopefully that will give him a massive boost for the next chance."
Liverpool finished the game against Oldham with 10 men when Daniel Agger left the field injured after Liverpool had already made three substitutions.
Toure knows injuries are part and parcel of football, insisting other members of the squad must now step up to the plate to compensate for the Dane's absence.
"We hope it's not bad news about Daniel," he said. "It's been a tough period with so many games and we're playing in such a tough league.
"Everybody in the squad always gives 100 per cent in training and in games and when you do that you can pick up injuries. It's part of the game. We have other players who can step in and play.
"When the league starts you know that anything can happen. We have to adapt and get on with it.
"It's really hard to get games here so when you have a chance to play you have to be ready. We need to keep winning."