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The Labour MP, who has been a critic of leader Jeremy Corbyn, said he recognised the party ran an "effective campaign" but a Conservative prime minister currently sits in No 10.
Questions should be asked about how the party can win a majority, he added.
The Tories have said they will form a government with the support of the DUP.
Speaking on the Today programme, Mr Leslie said: "We shouldn't pretend that this is a famous victory and, it's good as far as it's gone, but it's not going to be good enough."
He believes Labour still has "more to do" and the party needs to learn lessons so it can go on to win a majority.
Mr Leslie refused to say whether he thought Mr Corbyn was credible prime minister.
"I will never apologise for my view which is, yes of course you've got to inspire people and we haven't done that well enough in the past.
"But you've got to convince them of your credibility and that you can move from protesting about the government to being in government."