After Jummah prayer I was in a dilemma to either give my money to the poor(frequent visitors) or to give it for a construction of a masjid(one time visit). I ultimately gave it to the Masjid construction. Since Zakat is mentioned more in the Quran, should I have given it to the poor?
This is not zakat, this is charity. You must give your zakat out again to the 8 categories mentioned in the Quran. Give it to the poor and needy Muslims as Zakat must be given to a poor or needy Muslims in the form of cash to do with as they please.