Alexis Sanchez had already given the hosts the lead, profiting from a weak Steve Cook back pass, with Callum Wilson levelling for Bournemouth from the penalty spot soon after.
Theo Walcott toasted the birth of his second son by heading Arsenal back in front, with Sanchez rounding off an impressive display with a late third as the Gunners halted a run of three straight draws in November but Howe thought his side deserved better.
“I thought it was harsh on us, I thought we were well in that game,” he told reporters.
“We gave them the first goal and got a number of chances we didn’t take, the 3-1 scoreline is difficult for us to swallow.
“We have been unlucky, we feel there are a couple of incidents, I believe, have gone against us, I think every team will say that at the end of the season.
“I thought we were very good. It is always difficult when you go 1-0 down early on in the game, especially in that manner, an individual mistake.”
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.