"I think we've got to keep plugging away. These things can turn if we keep performing how we did today," Begovic told the club's website (afcb.co.uk).
"I was really pleased with the commitment, effort and desire so if we keep doing as we are then something (will) change. The key word is 'frustrated' as the boys did so well."
Striker Jermain Defoe saw a late effort blocked by Hugo Lloris as Bournemouth were denied a point, while Begovic made a string of saves but could not prevent a Christian Eriksen strike from slipping through on Saturday.
Bosnian Begovic said Bournemouth could be pleased with their discipline against the north London side.
"We worked hard, stuck to the game plan and were generally really disciplined. We had some chances, they had theirs and, unfortunately for us, one of theirs went in.
"That's the way it's going for us at the moment. We've not had so much luck in front of goal but we have to keep going because we're playing really well and we've got to keep these performances up."
Bournemouth visit Stoke City, who lost 7-2 to Manchester City over the weekend, on Saturday.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ian Ransom)
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