The Cherries came from a goal down to draw 1-1 at Dean Court.
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Tavernier said at the final whistle: "I feel like it was a scrappy game from start to finish, it was a tough battle out there.
"We knew in the second half we had to come out fast. The gaffer pointed out that we had to put in balls early.
"It's something we've worked on every week, especially as wide players putting the ball into the box for centre-forwards, and luckily it fell for Evanilson for his goal.
"We never give up. We know the first half wasn't ourselves. In the second half we knew we needed a reaction and we got that today.
"It's always the plan to try and win games of football. Today it wasn't meant to be but we dust ourselves down because we've got a quick turnaround."