The Black Cats boss felt nerves were to blame for his side’s below-par performance in Saturday’s 1-1 draw with Stoke.
The considerable consolation was the point they gained thanks to Jermain Defoe’s injury-time penalty, although Newcastle’s victory over Crystal Palace meant Sunderland dropped back into the bottom three.
Allardyce said: “I didn’t expect it.
“The lads are very, very good, they’re all supporting each other better than any team I’ve been involved with in the relegation fight.
“In the last few games, I hadn’t seen the sort of edginess I saw here, so we’ll have a talk about that in the week and try and get them to believe a little bit more in what they can do.”
Sunderland have three games left to save themselves for a fourth consecutive season.
First up is a home clash with Chelsea before their game in hand on Newcastle against Everton and then a trip to Watford.
Allardyce said: “Too many chances thrown away by ourselves has heaped more and more pressure on us.
“I still believe we should have beaten Arsenal last week and we’ve just not quite got enough sometimes to get over the line and to win the three points.
“I’ll try and calm those nerves next week and give the lads a nice week, not heap too much pressure on them, and try and get them ready mentally to go out against one of the bigger teams in the league, who’ve had a bad season but have still got massively talented players.”
If Sunderland do stay up, they will have one man to thank more than any other.
Defoe netted his 14th Premier League goal of the season after winning the penalty at the Britannia Stadium to make it 12 points his goals have earned Sunderland this season.
“He’s kept us in the picture, he’s kept us in a position where we can avoid relegation,” said Allardyce.
“He scores vital goals and I think the myth about not being able to play up front on his own has gone.”
Stoke boss Mark Hughes was left disappointed by the decision to award a penalty and the fact his side failed to win for a fifth successive match.
But the feelings were different to their previous three games, which had seen the Potters ship four goals each against Liverpool, Tottenham and Manchester City.
That led to accusations Stoke’s players were metaphorically on the beach — accusations Hughes believes they have now answered.
The Welshman said: “We’re not disappointed in the performance, the performance was good and a lot of players got somewhere near the levels that I know they’re capable of. That’s what I wanted to see so that’s encouraging for us.
“There’s no question that we’re not trying to see the season out in the right manner. I think we put all those comments to bed.
“We can still equal our most points in the Premier League so we still have things we want to achieve.”
Haugaard, Bardsley, Shawcross, Cameron, Pieters, Whelan, Imbula, Shaqiri (Diouf 78), Adam (Muniesa 86), Arnautovic (Walters 56), Crouch.
Joselu, Wollscheid, Krkic, Bachmann.
Mannone, Yedlin, Kone, Kaboul, Van Aanholt, Kirchhoff (Larsson 77), Borini (N’Doye 59), M’Vila, Cattermole, Khazri (Watmore 60), Defoe.
Jones, Rodwell, Pickford, O’Shea.
Craig Pawson (South Yorkshire).