Last December, the Reds relinquished a three-goal lead in the last 15 minutes of their Premier League away encounter with the Cherries to slip to a 4-3 defeat.
Jurgen Klopp's men went on to finish 17 points behind champions Chelsea after dropping 18 points from winning positions and conceding 42 times.
Former Reds defender Thompson hopes that his former club have learnt the lessons of that defeat as they seek to bounce back from successive Premier League draws with Everton and West Bromwich Albion.
"That game epitomised everything that went wrong last season," Thompson told Sky Sports News. "I was aware, with our vulnerabilities, it was too early to start celebrating.
"Then when it went to 3-2 I got a bit anxious. In these tight grounds you can really whip up a big atmosphere and suddenly put on a lot of pressure without much possession. We were very delicate at the time and it was probably the big let down of the season, so we owe these lot after what happened.
"That must be in the minds of the players, to learn from what happened, keep concentration and counter-attack better, although they have more attacking options this time with Jermain Defoe, along with Josh King and Callum Wilson."
Liverpool currently sit fifth in the table, having dropped the fifth-highest amount of points from winning positions in the league.