The Black Cats secured their first Barclays Premier League victory of the season at the 10th time of asking last Sunday, as arch-rivals Newcastle left the Stadium of Light on the wrong end of a 3-0 scoreline.
Allardyce was quick to warn his players that was only the start of his recovery mission - they remain inside the bottom three - and that there is still much work to be done.
But he does not want them to be bowed down by the pressure of what lies ahead.
He said: "It's a huge task for us all and we have got to meet it head-on, but we have also got to enjoy ourselves.
"It's depressing that a football club of this size with these facilities has only won its first game in 10
But it's about enjoying yourself and making sure that you look forward to coming in.
"Of course, that only gets better if you win football matches, but in the meantime, it cannot be all doom and gloom, it cannot be all depression because we will never get out of the problems we are in."
Sunderland travel to Everton on Sunday hoping to take advantage of the Toffees' difficulties at Goodison Park - Roberto Martinez's men have won only one of their five home league games to date this season - by completing a hat-trick of victories on the blue half of Merseyside for the first time in more than a century.
They do so with doubts over four key men - central defenders John O'Shea and Younes Kaboul, midfielder Ola Toivonen and striker Fabio Borini - but with confidence having been boosted by their efforts a week earlier.
Allardyce said: "Every time you get a result and when you get one as big as this, then the confidence grows in the team
But we have not to overshadow the fact that we have got to start playing better.
"As individuals and as a squad, we have got a fantastic result, but I'm sure we can play a lot better and we need to play a lot better to get more consistent results and make sure that we are very difficult to beat and that if we can't win a game, we make sure we can't lose it and keep picking points up in as many games as possible."
Source : PA
Source: PA