Pickford made his debut in the weekend's FA Cup defeat to Arsenal.
Pickford said it was his dream to play for the club and wants to push for the club's number one position, currently occupied by Vito Mannone.
He is quoted in the Chronicle, saying: “I’ve just got to wait for my chance and maybe be a little bit patient and when I’m called upon, grab it by both hands and hopefully don’t look back.
“The last thing I want to do now is go back out on loan.
“As a fan and a player, I want to be in the side and be number one, but I’ve got to be patient and try to put pressure on.
“I thought I made a couple of saves and my all-round game was alright considering I conceded three.”
Pickford may not get many other opportunities this season with Allardyce likely to keep picking Mannone ahead of him from now until the end of the season as the side looks to battle relegation.
However, there was nothing from Pickford's performance to suggest he has done any harm to his chances of more game time in the future - but it will all depend on Sunderland's season as to which level he will get those chances again from next season onwards.
Allardyce has said the goalkeeper has a bright future ahead of him so it is likely he will get opportunities in cup competitions at least if he is to stay at the club. But after several loan spells, there is going to be a thought of giving him regular game time at some point in the near future.