Should this pronoun be in the subjective or objective case?

[JohnDoe12345]

In the sentence "Let's play a game with you as the red team and me as the blue team," should the pronoun me be in the subjective case instead? If that be the case, why?

[5jj]

"Let's play a game with you as the red team and me as the blue team," should the pronoun me be in the subjective case instead?

'me' follows 'with'.