Maguire, the world number 28, will face England’s David Gilbert, ranked 31st, in the last eight but felt he needed to improve to become world champion.
“I’m still in it and I’m not going to say I’ve got no chance, but I’m one of the outsiders,” added Maguire, who once climbed as high as second on the rankings list.
“Being realistic, I still need to improve. I don’t think I’m good enough. I’ve not played good but got two good results when I’ve played better and lost.”
Both matches in the afternoon session ended at 9-7.
Stuart Bingham, the 2015 champion, held the edge over Jack Lisowski, taking the last frame on the pink ball to ensure he has the lead going into Monday’s final session.
On the other table, Northern Ireland’s two-time semi-finalist Mark Allen has the advantage over John Higgins after recovering from 7-5 down to win four frames on the bounce with breaks of 71, 94, 80 and 74.
Bingham and Allen both need to win four frames when their matches resume at 19:00 BST on Monday, while Lisowski and Higgins need six.
Kyren Wilson, the 12th seed and Crucible finalist in 2020, swept to a 10-1 victory over 52-year-old Dominic Dale in the first round and gained firm control of his last-16 match with Joe O’Connor on Sunday.
World number 30 O’Connor defeated fellow Leicester player and four-time world champion Mark Selby in a first-round shock, but he has it all to do on Monday against Wilson.
With a 10-6 lead, Wilson needs three more frames to set up a quarter-final with Allen or Higgins.