Second-half goals from Ryan Garry and Michael Symes earned Cherries a 2-0 win over the high-flying Blues at Dean Court on Saturday.
Garry's header and Symes's penalty helped Cherries maintain their fruitful start and also saw them leapfrog Carlisle to go third in League One.
Victory came after quotes attributed to Abbott in the Carlisle News & Star had been passed on to Eddie Howe's squad just an hour before kick-off And although most of his interview was complimentary about Cherries, Abbott was also reported to have said they had a soft underbelly defensively.
Assistant boss Tindall said: I am sure he didn't mean it to come across like it did, but, in some respects, it made our team talk very easy because we picked up on it.
Sometimes, you have got to try to use things like that as motivation for your own players. We have conceded goals in one or two games and are disappointed with that.
But I don't think you can accuse any of our players of having a soft underbelly. We've got some great characters and are a team of winners. I think they proved that against Carlisle.
Garry breached Carlisle's defence for the first time in more than six hours when he headed home Marc Pugh's 48th-minute corner to give Cherries the lead.
And Symes, on as a half-time substitute for Shaun Cooper, doubled their advantage from the spot after new loan signing Adam Smith had been felled by Francois Zoko.
Asked whether Abbott's comments had spurred on the players, goal hero Garry proffered a diplomatic response.
He said: With all due respect to the Carlisle manager, that is what we were told he had said an hour before we played his team. He might not have said it.
You don't like it when people say things like that but criticism is part of any profession and you have got to take it and use it the right way.
Carlisle are a good club and a good team and their record shows that. We were just happy to keep a clean sheet and win the game. That's all that matters.
Although Garry's goal was credited to him by referee Dave Phillips whose decision is final with the Football League the defender felt it may have been an own goal by Sean McDaid.
Garry added: I headed it down and thought it was going to get cleared but I think their lad might have kicked it on to his nose before the ball spun over the line. I don't know whether it was already over.
But Jason Pearce is still trying to claim one of the goals against Dagenham & Redbridge so maybe I should have this one!
In all seriousness, it doesn't really matter who scores. The main thing is winning, getting the three points and keeping a clean sheet.