Over the next two weekends, United face Arsenal and Chelsea, the two clubs locked in a tight battle with Spurs for Champions League berths.
"Having won the league, there's always a danger of falling into the trap of 'it's all over and we can relax' and enjoy ourselves but I think we've got a duty to other clubs who are chasing Champions League places," Ferguson told a news conference.
"Also, the rivalry we've had with Arsenal and then Chelsea over the years does put an edge to these games anyway so hopefully we'll represent ourselves in the right way."
His side travel to third-placed Arsenal on Sunday, where Arsene Wenger's side will form a guard of honour for them, and then host fourth-placed Chelsea the following weekend at their Old Trafford ground where they secured a 20th title this week.
With last year's champions Manchester City closing in on the runners-up spot, it leaves two Champions League places for the chasing pack of Arsenal on 63 points, Chelsea on 62 and Spurs on 61. Arsenal have played a game more than the other two.
Everton, on 56, are mathematically, if rather unrealistically, also involved.
Ferguson said he would field a strong side for the trip to north London, where top scorer Robin van Persie could face boos from fans at his former club.
"We have a few bumps and bruises from the other night but it is hopefully nothing serious and I expect to have a strong side on Sunday," Ferguson said.
Motivation also comes from the record points total that United are still chasing and they know if they win their four remaining matches they would surpass the mark of 95 set by Chelsea in 2004-05.
Van Persie, whose hat-trick against Aston Villa on Monday secured the 3-0 victory that clinched the championship, also has a second successive golden boot in his sights as he tops the scoring chart with 24 league goals.
Luis Suarez, his closest rival with 23, will not play again this season after the Liverpool striker accepted a 10-match ban for biting Chelsea's Branislav Ivanovic, giving Van Persie the opportunity to run away with it.
Ferguson said he was pleased Wenger had followed tradition with his decision to form a guard of honour and that he was not worried about what sort of reception Van Persie might get.
"I don't think Robin should bother about it either," he said.
"There was some booing of him when he played against Arsenal at Old Trafford and I think you probably expect a portion of the fans will do that. But that's the modern generation and modern society, I'm afraid."
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