Speaking ahead of Saturday's league visit of Brighton and Hove Albion, Allardyce was asked if he wanted to manage the club beyond the end of the season.
"Of course. There's tough times and there's times when you have to draw in, close the doors and stay focused on what you want to achieve," he told reporters.
"It's very disappointing for everybody that we've slipped to where we have slipped to after the fantastic position we put ourselves in the early stages of me walking through the door.
"I came out of retirement because there's a long-term plan at Everton that I was excited to be a part of... I know all about Everton and what you have to try and achieve."
Everton will be without suspended defender Ashley Williams on Saturday but Allardyce is set to have fit again Ramiro Funes Mori and Phil Jagielka available to fill the void left by the Welshman.
"We have got Funes-Mori back after a couple of Under-23 games," the manager said. "Mangala is unfortunately injured until the end of the season but we have got a number of centre-halves we can choose from."
Following back-to-back away defeats at Watford and Burnley, Everton have dropped to 11th in the league but Allardyce believes a seventh-place finish remains an achievable target.
"We have to turn our away results around if we're to get into that position," he said.
"We put ourselves in a position to achieve that and have failed to kick on. I want to get the next two wins to achieve safety but you can still finish seventh if you have a good end to the season with four or five wins."
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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