The Scottish champions cruised to a 5-1 win at Kilmarnock yesterday to seal the three points that secured them their third straight championship.
The success came against a backdrop of difficulties, from lack of cash and a small squad battling against injuries to months of uncertainty over the future ownership of the club before Craig Whyte finally completed his protracted takeover.
Whittaker said: "We are football players at the end of the day and we are paid to play football.
"It's not the biggest depth of squad we've ever had but the boys dug in together. We're a close bunch and I think the character to win shone through in the end. Our attacking flair over the last three or four games has been tremendous. The finishing of some of the goals has been top notch."
Kyle Lafferty set the ball rolling after just 47 seconds at Kilmarnock, before Steven Naismith doubled the advantage and Lafferty claimed his second of the day all in the opening seven minutes.
Nikica Jelavic added to the goal haul early in the second half, before Lafferty sealed his hat-trick and Whittaker added: "We wanted to start fast and start well and, if we had scored one goal in the first ten minutes, we would have been happy.
"To score three in seven minutes was unbelievable. It was a bit of a blur and a great start for us. The aim at the start of the season is to win the championship and to do that is a special feeling."
Whittaker believes Allan McGregor's penalty save in the final Old Firm derby of the season and Celtic's recent defeat at Inverness were pivotal moments in the title race.
He said: "Allan's save kept us within touching distance. Even drawing that game, it was out of our hands and it was down to Celtic.
"They slipped up at Inverness and it came back to us. We had three games to go and knew we were capable of winning all three."
Meanwhile, Lafferty accused Celtic of failing to deliver the goods when it really matters. He said: "I think we have been the better team. Even when we were not playing well, we were still picking up points. That's one thing that Celtic can't do; when the going gets tough, that's when they fail.We've got the heart and desire in the team to go out and win games."