Manchester United manager Ole Gunnar Solskjaer said it was a "step back for us" as his side's three-match winning run ended at Bournemouth.
"If you want to get into the top four you need to win games like this," said Solskjaer.
"I am frustrated on one hand, but on the other hand we could have also lost the game," manager Eddie Howe said.
"Keeping a clean sheet away from home is positive, but having our third game without scoring is certainly negative.
Eddie Howe said Bournemouth's victory over Everton was a "huge moment in our season" as Callum Wilson scored twice at Vitality Stadium
"Psychologically, it was hugely important to win that first home game which is why today was a huge moment in our season," said Bournemouth manager Howe.
Jamie Vardy scored twice and made the other as an impressive Leicester maintained their unbeaten Premier League start by easing past Bournemouth at King Power Stadium.
Brendan Rodgers' side have won two and drawn two of their opening four games, showcasing their early ambitions of breaking into the top six at the end of the season with another excellent showing.
Manchester City made quick work of Bournemouth as Sergio Aguero scored his 400th career goal. Aguero leads all 2019 Premier League goal scorers, and along with the immense contribution of David Silva, the old guard of Manchester City prove they still have plenty left in the tank.
Bournemouth vs Tottenham Hotspur Highlights
Start date: 04. May 2019, 12:30
Location: Bournemouth Venue: Vitality Stadium
Referee: Craig Pawson, England
Nine-man Tottenham conceded an injury-time goal to lose 1-0 at Bournemouth, narrowly failing to hang on after having Son Heung-min and Juan Foyth sent off in a five-minute span around halftime
Goal by Aké at 90+1' gets Bournemouth a victory.