Phelan was put in temporary charge of the team after Steve Bruce left in July and he was handed the role on a permanent basis this week.
"We all know that we have got a job to do and it's a hard job, and this will be a difficult job, trying to get this football club to stay in this Premier League," Phelan told Sky Sports.
"We are under no illusions, that's the aim, that's the course we are going to go on," he added.
"But we also want to try and change a few things on the football field as far as performances go and as far as team spirit and the collective element of the club."
Phelan said he was relieved to get the manager's job after weeks of negotiation.
"It is a relief because when you have got something hanging there by a thread sometimes," the 54-year-old said.
"I would be a liar to say that I didn't have my doubts. It just kept swinging to and fro all the time and it was just making sure that all the conditions were in place that could help me push this football club forward."
Hull, who are 15th in the table, travel to 13th-placed Bournemouth on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
