The Foxes shocked the Red Devils at the King Power Stadium as they rallied from 3-1 down midway through the second half to run out 5-3 winners.
Phillips feels that the result is a testament to the character of the players in Nigel Pearson's squad.
He told Sky Sports News: "We have a never-say-die attitude in abundance here, as well as great work rate and commitment. We believed we could still create chances and the lads were outstanding.
"Then, how many teams who got back to 3-3 against United would sit back and settle for a point? That's not in our make-up.
"We felt we could go on and win the game and I don't think anyone could have any arguments if I said we thoroughly deserved to win it in the end."
Leicester are seventh in the Premier League with eight points from five matches.