Defoe scored 11 times in 25 league appearances last season and has been named in Roy Hodgson’s 23-man squad for the upcoming tournament in Poland and Ukraine, but may leave Spurs in search of regular first-team action.
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"It is a difficult one. I have never said I want to leave the club, all I have just said is I want to play," he told talkSPORT.
"As a forward you just want to get some sort of rhythm and a run in the team. That wasn't the case towards the end of the season.
"I am going to concentrate on England and go to the Euros, then see what happens. The most important thing for me is scoring goals and that is when I am at my happiest."
Spurs finished fourth in the Premier League which would usually be enough to secure Champions League football, but Chelsea’s dramatic win over Bayern Munich means Harry Redknapp's side will instead compete in next season’s Europa League.
However, the former West Ham striker believes the club should be happy with their league finish as they managed to achieve their target set at the start of the campaign.
He added: "The main aim of the season was to finish in the top four, and we have done that. What happened with Chelsea was out of our hands and was just unfortunate.
"There have been lots of ups and downs, but we all stuck together and still performed."
A lack of Champions League football next season has heightened speculation linking Luka Modric and Gareth Bale with big-money moves away but Defoe believes the club need to keep them hold of them.
He continued: "In football you never know what is going to happen, but it is always important to keep hold of your top players.
"Some players like Luka Modric and Gareth Bale are players you cannot replace, so it is important to keep them."