Sunderland are currently fighting against relegation from the Premier League with just two games remaining.
Their hopes of survival were given a huge boost on Saturday afternoon as they beat Chelsea 3-2 at the Stadium of Light.
That saw them move into 17th place in the Premier League and they can now secure their survival, and rivals Newcastle’s relegation, with a win over Everton in midweek.
It was the culmination of several impressive performances in recent weeks, and Allardyce says the immense character of his squad has finally shown through.
"The immense character of the team has shown through," he told BBC Sport.
"The recovery was magnificent. Everybody has played their part. You often wonder about the characters of your players. For the first time this season we've recovered from two blows by going behind twice."
Sunderland will now be confident of securing their Premier League survival against a lacklustre Everton side in midweek.
The Blues are limping towards the end of the season, and the loss to Leicester City at the weekend seemed to show that they have already given up.
That is perfect for Allardyce’s side, who know that their Premier League status is very much in their own hands and should they fail to maintain it, it is solely their fault.