The Spaniard finally opened his account on his 11th appearance for the Reds with the crucial first in the 2-0 FA Cup win over League One Oldham.
It ensured he avoided joining El Hadji Diouf as the only Liverpool number nine to go a whole season without scoring.
While opportunities have been limited for the 26-year-old because of the form of Luis Suarez and Daniel Sturridge and also a thigh injury, there was a feeling he had not made the most of the chances he had been given.
Aspas is never likely to dislodge either of the two front-line strikers but Toure thinks his breakthrough goal will make a difference to the player who still has plenty of time left to contribute this season.
"This goal will change him, definitely," said the Ivory Coast international, himself starting back-to-back matches for the first time since November.
"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."
Aspas, who has found himself filling in positions on the forward line he is not entirely comfortable with, felt being given the chance in his preferred central role helped him.
"I played the last game on the right wing and (against Oldham) I played as a striker, which is my position," he told www.liverpoolfc.com.
"It's wonderful for me to score my first goal here.
"It's difficult when you don't play all the games, but I'm very happy to have scored."
Winger Raheem Sterling provided the assist for Aspas' goal, also crossing for the Spaniard to head against the post and later seeing his shot deflected in by defender James Tarkowski for Liverpool's second.
He has had his own peaks and troughs since breaking into the first team in 2012 but his form appears to be back on the rise again having started the last nine matches and he is well-qualified to comment on Aspas' fortunes.
"It will give him a big boost," said the 19-year-old about the Spaniard's goal.
"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."
On his own form, Sterling added: "I'm enjoying it massively and the manager has put his trust in me to put me out every week so far.
"Hopefully I can deliver on the pitch and get some more assists and goals for the team."
One negative from the Oldham victory was injury to defender Daniel Agger.
Manager Brendan Rodgers said cramp in his calf forced the Dane off late on - and left Liverpool with only 10 men as they had used all their substitutes - but the player's immediate reaction in saying he could not carry on suggested otherwise.
Liverpool are awaiting an update but Toure believes injuries, of which there have been a few this season, are just something they have to deal with.
"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."
Rodgers has not been able to field a consistent back-four after injuries to Jose Enrique, Aly Cissokho, Glen Johnson and Mamadou Sakho this season but Toure said nobody was looking for excuses.
"It's not easy when you have to make a lot of changes but that's what pre-season was for - to get everyone used to playing with each other," he added.
"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."