Albert Barnes Commentary Psalms 78:22

"Because they believed not in God, And trusted not in his salvation." — Psalms 78:22 (ASV)

Because they believed not in God - They did not believe in his power, or in his promises.

And trusted not in his salvation - In his power and his willingness to save. They had had abundant evidence of that power, but they still doubted his ability to save them, despite all that he had done for them.