The Wales international produced a moment of magic to score the winner against Sunderland on Sunday but his effort was rendered meaningless as Arsenal were 1-0 winners at Newcastle United.
With the Gunners finishing one point ahead of their north London rivals and securing the final Champions League spot, Spurs are faced with the prospect of another season in the Europa League.
And PFA player of the year Bale, who has scored 21 Premier League goals this season, couldn’t hide his disappointment at missing out on Europe’s premier club competition.
“It was obviously great to sign off with a great goal in the last minute, but circumstances made it hard to celebrate,” Bale told Tottenham’s website.
“To play the way we have also but to miss out on our objective [Champions League qualification] is very disappointing.”
Bale picked up Tottenham’s player of the year award to complete a unique treble after winning the PFA and Football Writers’ Association’s equivalent earlier in the season.
And the 23-year-old, who has been linked with a move away from White Hart Lane this summer, promised that the north London side would regroup over the summer before another assault on the top four next term.
“We fought hard this season, the team and the manager have been great,” Bale added. “We have got the record points for the club in the Premier League.
“That would normally be enough to qualify for the Champions League, but it’s not meant to be again.
“It’s disappointing, but we will pick ourselves up again.
“We will just have to regroup this season and give it another go.”
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