Wales defender Ben Davies equalised for Tottenham with his first goal of the season
The visitors showed hunger and resolve to recover from two goals down, clinching victory when second-half substitute Rodrigo Bentancur pounced quickest in the second minute of stoppage time.
"It was great to see the desire of my players and the reaction they had," said Conte, whose side need a point at Marseille to reach the last 16.
"Also, the nastiness they put into the pitch because I have seen in the eyes of my players the desire to win this game.
"It was important to win this game. I think we showed good character."
Initially Spurs were flat as Bournemouth looked set to end a run of two successive defeats.
Wales international Kieffer Moore, making a rare start, swept the Cherries ahead following a flowing counter attack.
His second was more about guts than guile as he outmuscled Emerson Royal to meet Adam Smith's cross with a powerful header which went in off the bar.
Spurs rarely threatened before Ryan Sessegnon narrowed the gap with a cool finish into the bottom corner.
That sparked a shift of momentum and Spurs levelled when home keeper Mark Travers made an unconvincing attempt at claiming a corner, allowing Ben Davies to head in from Ivan Perisic's delivery.
Spurs continued to press and were rewarded when Bentancur reacted quickest to sweep in from another set-piece.
The relieved celebrations at the full-time whistle, from both the Spurs players and the travelling support, illustrated the importance of a morale-boosting win.
"My feeling [when 2-0 down] was we still had the possibility to win this game," added Conte.
"When we suffered in the first half I told my players it is on us. I asked for more personality, more responsibility and more decisions.
"My players showed great character and great desire and didn't accept defeat. In the end we deserved to win because we created chances."
Tottenham remain third in the Premier League table after recovering to beat Bournemouth, yet lingering questions remain about the issues faced by Conte.
With almost an hour on the clock, it looked like a bad week for Spurs - who were beaten by Manchester United and Newcastle before a controversial draw against Sporting stopped them securing a place in the Champions League last 16 - would get even worse.
Discussion about whether the Italian's tactical style is stifling Spurs' attacking talent, and why they continue to start slowly, remain.
But his side, which featured seven changes with one eye on the trip to Marseille, certainly cannot be accused of not showing fight.
Spurs dominated possession in the first half but lacked creativity as they barely tested Bournemouth's stand-in keeper Travers.
They were made to pay as Bournemouth took control but Sessegnon's strike, which came out of almost nowhere when he latched on to Pierre-Emile Hojbjerg's incisive pass, provided much-needed impetus.
Conte has talked about his team lacking belief and, with Harry Kane and Son Heung-min relatively well contained, Spurs were unable to create a lot from open play.
Eventually, it was set-pieces that provided the breakthrough and allowed Spurs to go to Marseille in higher spirits.
The mood around Bournemouth has been transformed by interim manager Gary O'Neil, who took over following the 9-0 defeat at Liverpool in August and immediately led the newly promoted Cherries to a six-game unbeaten run.
Progress was stalled by back-to-back defeats at Southampton and West Ham, but it looked like O'Neil's side were going to get back on track against Spurs.
For large periods they coped well with what Spurs managed to throw at them.
But once Davies equalised after Travers was weak in coming off his line, the home defence suddenly looked uneasy in dealing with Spurs' set-pieces.
Tottenham's 19th corner of the game, deep into stoppage time, led to second-half substitute Bentancur heading at a Cherries defender before firing in the rebound.
"Conceding from set-pieces against a team like this is unforgivable," said Cherries defender Jordan Zemura, who took responsibility for not marking Davies tighter.
"It's something we need to sort out. We know we need to be better. It is a collective."
Despite a third straight defeat, O'Neil - whose future is still unclear with the club's takeover by American businessman Bill Foley close to being completed - said he was not unduly worried.
"We've had some tough games, with this being the toughest," said O'Neil, who took over from Scott Parker following the heavy defeat at Anfield.
"There is a gulf between us [and Spurs] and we did everything we could to close that gap. We made it competitive and Spurs had to dig very deep."
-- Courtesy of BBC Sport