The Black Cats were struck down by nerves in the first half of the 1-1 draw with AFC Bournemouth at the Stadium of Light, the pressure gauge cranking up a few notches after Benik Afobe’s 13th minute opener.
Sunderland have the worst record in the league when it comes to conceding early in Premier League matches.
And Allardyce has called on his players to show their experience and not be drawn into situations where they invite pressure onto them.
Eddie Howe’s Cherries had scored seven goals in the first 15 minutes – the most this season – while Sunderland had conceded eight in the same period, so the warning signs were there.
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Patrick van Aanholt rescued a point but conceding early goals is crippling the club’s attempts to stay in the top flight.
Allardyce would rather his players avoided trying to play their way out of trouble and instead get the ball up the pitch with greater urgency, especially early on in games.
“We started okay until they scored the goal,” said Allardyce.
“There was eight or nine minutes when there was nothing in the game until they scored, then the nerves went a bit.
“At this level why complicate the game and overplay?
“When you are struggling put the ball in the opposition’s half with a bit of quality, squeeze up away from your own goal and press them to try and win the ball back.
“That relieves the pressure, the closer they get to our goal the more the nerves jangle.
“That was disappointing because we had a lot of experienced players out there who should know how to deal with it in those positions.
“Our persistence in playing one-two passes and continually seeing them cut out, meant we should have said ‘forget that’ lets squeeze up and get in their half.
“Even if it means getting them turning and running towards their own goal, kicking it out for throw-ins.
“Our goal came from a throw in. A great goal but it came from a throw-in initially, and you could see the difference as the nerves healed and our confidence came back.
“A tactical change putting Adam Johnson in the middle made a huge difference, Jeremain Lens going out wide.
“We just couldn’t find a perfect ball for the wee man to get a chance to score, who might have won it for us.”
The draw, coupled with defeats for Norwich City and Newcastle United, has left Sunderland four points from safety.
And with a daunting run of February fixtures to come, the situation looks bleak with title-chasing Manchester City next up at the Stadium of Light a week today.
Allardyce was pleased the south coast outfit didn’t pull any further away from Sunderland. But he is under no illusions as to the task facing his players, who secured only their first draw under him against the Cherries.
Wins are needed and Sunderland are going to have to spring a Premier League surprise of their own at some stage if they are to battle they way to safety.
“We have our first draw, Bournemouth are no further away from us and we move on,” added Allardyce.
“We are still in a very difficult position and we need to change that as quickly as we can.”