Are "not because" and "not just because" opposites?

Solution 1:

Your second interpretation is nearly correct: the team are hampered by the suspension of their key players and the implication is that they are still motivated. However, even if they are not motivated, the speaker says that the suspension is the cause of the poor performance.

"...not just because they have lost motivation..." doesn't just suggest that the team has lost motivation, it positively states it and also states that the loss of motivation contributes to the loss of performance. However it also states that the suspension contributes to the poor performance.

To turn the situation on its head we can say "They aren't playing as well as they usually do, not because their key players are suspended but because they have lost motivation. In this case we would be dismissing the obvious problem (the suspension) and saying that the cause of the poor performance is a loss of motivation on the part of the team members,