Pep Guardiola’s side made a winning start to a run of three crucial fixtures with a 1-0 victory away to Crystal Palace in the Premier League on Saturday.
RB Leipzig come to the Etihad Stadium on Tuesday, 14 March for the Champions League last-16 second leg with the tie finely poised after a 1-1 draw in Germany before an FA Cup sixth-round clash with Burnley on Saturday, 18 March.
“It’s always the aim every season – every competition we try and go right until the end and win everything,” Stones said.
“That’s the standard we’ve set as a club and as a team. We’ll go for everything and hopefully we can come out on top.
“We’ve got to take it one step at a time and take each game as it comes. It’s down to us – sometimes we are our own biggest enemies. We don’t concentrate on the outside or anything that’s going on.
“It’s about us and what we can do. [Yesterday] was one of those games where we did everything right and we move onto the next game.
“Everyone is excited in the dressing room – especially with the Champions League and see where we can take it. We’ve got to focus everything on that now and see where we can go.”
City had to be patient at Selhurst Park before picking up the three points after Erling Haaland coolly tucked away a penalty in the 78th minute.
Stones believed it was a well-earned victory and says City must continue to maintain their composure as we have done in previous trophy-winning seasons.
“We’ve got the experiences and obviously new players have come in and settled in so well,” he added.
“We’ve got to stay calm and control what we can control. [Yesterday] was one of those things where we knew it was going to be tough and we had to come out on top of it.
“We said before it was a vital game we needed to win, and we dealt with that and came out on top.
“We want to keep this winning run going and to keep contending and keep pushing for titles or whatever competition we’re in.
“We need to come to difficult places and play against top teams and beat them – it was one of those tests where it was different to normal, maybe a bit more of a dogfight.
“How we dealt with them, and their threats and strengths is a credit to the boys and the team and how we all worked together. We kept out heads and kept playing our football.”
The game was Stones’ first appearance since January after suffering a hamstring injury in the FA Cup win over Arsenal and the defender was delighted to be back.
“It’s always frustrating when I get an injury,” he said. “I worked really hard to come back better and stronger and hopefully I can keep progressing and contributing and see where it takes us.
“There’s a lot of games to play still and everyone is a vital part in how the team and the manager works. We’re all going to play games and contribute."