Sunderland have seized the initiative in several matches, before throwing things away in the final minutes, and they were guilty of letting a lead slip again in the Tyne-Wear derby.
The Black Cats had gone in front at St. James’ Park when Jermaine Defoe struck in the early stages, but a late header from Aleksandar Mitrovic meant that the points were shared.
The goal was a devastating blow for Sunderland’s survival chances, but Allardyce is pleased that his side are, at least, getting in positions to win matches.
"The consolation for me is that we have been in a position to win every game, particularly when we score first and we do things right by taking control of the game," he said.
“We are just not managing to see that through and turn it into a victory, and that’s the thing we have to try and change.
“We have to change it right now.
“We are now in a position of must-win – draws are not going to be good enough for us now."
Sunderland also conceded in the last minute of their match against Southampton at the start of the month, and their failure to hold on could prove costly.
Allardyce’s side are currently in 18th place in the Premier League table, and they are two points adrift of safety.
Sunderland’s next match comes against West Bromwich Albion on April 2nd, where they will be looking to show greater defensive solidarity to secure the three points.