Neil Lennon acknowledged the absence of Rangers from the Scottish Premier League title race this season had made life easier for Celtic after it finally picked up the trophy.
The Hoops thumped St Johnstone 4-0 at Parkhead before celebrating with the silverware.
The Ibrox club emerged in the Irn-Bru Third Division last year after descending into administration and liquidation, which effectively rendered the SPL title race little more than a procession for the Hoops.
In the event, there were ups and downs this season before Lennon's side retained the title with a 4-1 win against Inverness three weeks ago.
The Parkhead club confirmed its superiority against Saints with goals from
"We have proved we are not a flash-in-the-pan team," said the Northern Irishman, who, in his after-match speech to the crowd, referred to Celtic's "unique and unbroken history."
"I know there will be a lot of people out there saying there is no Rangers, it is a one-horse race and in essence there is something to that.
"We are not going to hide away from that but we have a job to do.
"We have a responsibility to keep winning trophies, it is part of the DNA of the club and to do it in a certain way.
"Since the turn of the year the home form has been as good as I've seen in my time here.
"We know we need to tidy up away from home but the league is won now and we can focus on finishing the season with a cup final."
Lennon, who spent the last few days fending off speculation about him taking over from
"It is a long way off," said the former Celtic skipper. "The next target is the third. We will take it step by step for that.
"You can never take football or these achievements for granted. "There is a lot of work goes into it, 10 in a row is a long, long way off.
"Eventually Rangers will come back and they will put in a challenge over the next few years, I would imagine."On the Everton speculation surrounding his gaffer, captain Scott Brown said: "Of course we want him to stay. He has been great for me.
"The gaffer loves the club and he enjoys coming in every day and he shows is enthusiasm at the side of the pitch."
Scottish Premier League
Kilmarnock gave its hopes of avoiding the Scottish Premiership's relegation play-off spot a welcome boost with a 4-2 win over bottom side Heart of Midlothian at Rugby Park.