Three wins from three to start the league campaign for the first time since 1991 for the Dons but defender Ash Taylor knows the challenges are only going to get harder.
The Dons rallied from the loss of an early Marvin Johnson goal to defeat Motherwell 2-1 at Fir Park on Saturday with an equaliser from Niall McGinn before the defender headed the winner in the second half.
The 24-year-old is determined last season’s second-place finish was not the highlight but knows the Dons are now a prized Premiership scalp.
He said: “Teams will give us a bit of respect because they know we are a good side. But three wins from three to start the season is excellent, although we have to maintain that.
“We did well last season but we just want to improve this time around. We need to maintain a level of performance and make sure it takes us up the league.
“We are stronger as a team. We have been together for a year and brought in some good players, experienced players.
“Motherwell made it difficult for us at times but we dominated long spells of the game and we deserved to win.
“We don’t expect to win games but, with the players we have in our squad, we can cause a lot of problems for others and are capable of scoring goals, we just need to work on keeping clean sheets.
“We never know when we are beaten and the spirit in the squad is strong.”
Strength in the Aberdeen squad will be hugely important if the Dons are to challenge Celtic for the title and Taylor added: “Adam Rooney not starting on Saturday shows how strong the squad is as he scored nearly 30 goals last season.
“Although it is really early in the season we know we have got to maintain our level of performance and get as many points as we can as quickly as we can. It’s any team’s ambition to go that bit further and improve each season.
“We don’t set targets throughout each quarter of the season, we just want to improve and if that means more points to get us closer to Celtic then so be it.
“I got five goals last season, so hopefully I can get a few more this time round although my job is keeping clean sheets.”
Victory came at a price for Aberdeen, with midfielder Willo Flood suffering an ankle injury.
Manager Derek McInnes said: “His ankle swelled up and he had slight ligament damage but we don’t think there was too much damage to the structure. Hopefully, it’s nothing too serious.”