Scott Brown insists Celtic will not let their focus drop despite having secured the club's fourth successive title.
And Brown, 29, admitted the Dons' challenge had pushed Celtic on.
"We need to make sure that we're focused, not sloppy and keep trying to win games to get as many points as possible," said the club captain.
"It was a good challenge from Aberdeen. It's always hard but we kept fighting and playing good football. That's what we try to promote at this club.
"You always look at whoever's second or third. At the start of the season we were playing catch-up and knew we had to win games to put Aberdeen under pressure and we managed to do that.
"They always make it hard at Pittodrie but it kick-started our season going up there and winning, scoring in the 91st minute [in November].
"You always look at the league and worry why we're not top with the squad and the talent that we have. The gaffer [manager Ronny Deila] had his own style of play and it slowly and steadily got in there. We're enjoying every single moment now and it's coming together nicely.
"Everybody always assumes that we're going to win the league but it's hard to go and win games week in, week out, especially with Europe as well. We still managed to do it."
Scotland midfielder Brown also spoke of his delight that Deila, who took over from Neil Lennon last summer, had led Celtic to success following a difficult start to his career at the club.
Celtic, who face Aberdeen at Pittodrie on Sunday, were knocked out of the Champions League qualifiers before having a Europa League run to the knock-out rounds and also dropped points early in their domestic campaign.
"He [Deila] was under a lot of pressure," Brown explained. "He's dealt with it unbelievably. He enjoys the club, the spirit and the surroundings.
"He understands it's all about winning at this club. He wants to play good, attractive football, but if the pitches aren't good you can't play attractive football and you've got to win the battle before you get the ball down."
Gary Mackay-Steven, one of Deila's winter transfer signings from Dundee United, featured in the Europa League last 32 aggregate defeat by Inter Milan and is eager for more European matches.
"That was incredible to be part of that and taste at first hand European nights at Parkhead," said the 24-year-old winger.
"They're special and we want to bring Champions League football back here.
"Now the manager has a wealth of options in all the positions and to play you need to grab your chance with both hands.
"Looking ahead to next season, there's so much to play for and you have to hit the ground running."