The 23-year old, who has netted 10 League One goals so far this season, was not called up to the Scottish squad for last Tuesday's friendly with Norway despite a trio of attackers pulling out because of injury.
Griffiths tweeted: "Gutted with three call offs and I ain't got called up to the squad."
His club manager Jackett, who has seen Griffiths score in six wins this campaign, felt the former Hibernian loanee was fair in his criticism of the Scotland squad but urged him to work harder to force his way back in.
"We do say to the players to be careful what they tweet and make them aware of that. But the other side of it is that this is a free country and for someone who is 23 that is their way of expressing themselves," said Jackett.
"The best thing he can do is go out and get another 10 goals and keep knocking on the door.
"He has had a taste of it and knows he can get in there, that is one good thing.
"As a manager you need to look at different combinations to see if you have got an even better one and you still know that the other one is there.
"So it is in Leigh's hands. He is young enough to get back in.
"He has worked well here in training and so far this season he has been terrific and we have been a better side with Leigh Griffiths in it that out."
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