Can I travel to Panama as a Pakistani and US resident?

Of course you can enter, mostly anyone can with the appropriate documentation. In your specific case, Pakistan is not in the list of exempt countries (Spanish).

But since you have a Green Card, you should be exempt based on the Visa Waiver Executive Decree, emphasis mine (Source):

Visa Waiver

There is a Law in effect regarding tourist visas for entering the Republic of Panama;

EXECUTIVE DECREE # 591 states that: “Those who hold a valid passport with a 3 months validity left and a multiple entry visa with a remaining ONE year validity from ONE of the following countries: USA, Australia, Canada, or United Kingdom, which has been used at least one time to enter these countries, may enter the Republic of Panama regardless of their nationality” For more clarification you will qualify for this decree if you comply with all of these requirements:

Have a valid passport with a minimum of three months of validity left.

Have a multiple entry visa with a remaining ONE year validity from ONE of these countries: USA, Australia, Canada, or United Kingdom.

You must have used this visa to enter the country. For example, if you have a United States Visa, you must have entered the U.S. with that visa in order to qualify for the waiver.

Immigration officials are accepting as valid the entrance of the holders of a United States permanent resident card under this law.

You must also show proof of economic solvency for a minimum of US $500.00 upon entry. NOTE: Please make sure you have a minimum of three months of validity left on your passport and a round trip ticket.

For further information please access the following link which contains a copy of the law decree :

https://www.gacetaoficial.gob.pa/pdfTemp/28196_B/59547.pdf

Reading the Gaceta Oficial, Article 1 states this as well. The header of the decree also affirms that this applies for tourist visas.