Two goals from David Bentley and one from Tugay gave Blackburn a 3-1 victory on Saturday, after Obafemi Martins had opened the scoring.
The setback was Newcastle's fourth defeat in five matches and a home defeat to league leaders Arsenal on Wednesday night could result in the end of Allardyce's six-month reign at St James' Park.
The Sunday Times claims defeat would "almost certainly see Allardyce lose his job, and Alan Shearer take over the coaching role".
However Allardyce was pleased with his side's performance at Blackburn and now wants them to reproduce it over the next two games he believes could shape their season.
He said: "We have got to play like we did at Blackburn when we are next at home.
"Then you will get support from 52,000 fans. They do not want to see players playing poorly.
"We had a good performance from 11 individuals against Blackburn and did not deserve to lose.
"It keeps the bad run going and can eat away at your confidence. But my job is to make sure we maintain this kind of spirit and commitment, combined with our ability.
"That's what is needed if we are going to turn things around and get some points on the board."
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