The Baggies have endured a tough start to life back in the Premier League with back-to-back defeats to Leicester and Everton.
In both those games they have performed well in the first-half.
But they've conceded too many poor goals after the re-start – with Kieran Gibbs' red card at Everton on Saturday not helping their cause.
And Livermore says they can't let silly mistakes blight their season.
"We don’t want that to be the story of our season," the captain said.
“We’ve started well in both games and unfortunately pivotal moments, whether that be goals, decisions or sending offs, we seem to be getting on the wrong end of them and we can’t let that creep into our season.
"We need to learn fast and nullify those mistakes.
"We need to learn quickly The boys have shown some good quality and some good stuff. it’s a case of stretching that out over 90 minutes.
“Some decisions we've been on the wrong side of, but that’s football. We need to put ourselves in a position where those decisions don’t make so much of a difference to the result.”
Meanwhile, former midfielder Gareth Barry believes the Baggies need to back head coach Slaven Bilic in the transfer market.
The Baggies have signed Matheus Pereira and Grady Diangana – players who were on loan last season – as well as David Button, Cedric Kipre and Conor Gallagher so far this window.
But Button and Kipre are squad players. And Barry feels Albion need to improve their starting XI.
"The players they have signed are good players and were really important last season," Barry said.
"But the bigger picture is that they have not improved the team.
"We got up from the Championship but for anyone who comes up, you have to look to improve that squad.
"At the minute they have probably not done that.
"They had to spend on Pereira, Diangana – players that could potentially turn into world class players. For the future, they are very good players.
"But it’s going to be a tough initial test in the Premier League for that squad I feel."