The Cherries will now go into their final game of the campaign against Leicester City knowing that a victory will guarantee a place in the top half, and Cook urged his side to make one last push.
"We have got one more game and the incentives are still there for us to finish in the top half, but I thought we were very professional and topped off a good home campaign here [against Burnley]," he told the club's official website.
"It is always difficult, a lot of sides do have a big strong centre-forward. Every game is different, we defended well as a team. It is a shame we didn't get the clean sheet but overall I think we are very pleased."
Bournemouth's previous highest ever finish came last season, when they ended up 16th in the top flight.