The former Arsenal defender believes the 'emotion of the occasion' got to the Reds.
The Reds finished second by just two points last term, when Manchester City won the second Premier League title in their history.
It could have been Liverpool's first league trophy for 24 years - and their first Premier League championship - but the Anfield side fell short in the closing stages of the campaign.
When a 0-0 draw at Chelsea would have been enough to keep them in pole position, they lost 2-0 to Jose Mourinho's men, before surrendering a 3-0 lead at Crystal Palace to draw 3-3.
And Keown believes the Liverpool players let the emotion of the occasion get to them in their bid for league glory.
Indeed, when asked - as part of his Tackle Keown session on the Daily Mail - about Brendan Rodgers' side's Champions League win over Ludogorets, Keown said:
"Liverpool were not at their best either and you wonder if the emotion of the occasion tripped them up.
"That level of emotion is okay as long as you can handle it but it almost cost them the title last season.
"As a player, you have to let the fans be emotional and you must stay professional."