Brighton's Glenn Murray and Solly March scored in a 2-1 win over Wigan Athletic in the Championship on Monday to secure the south coast team's return to the top flight after a 34-year absence.
Promotion to the Premier League is set to provide a major financial boost to Brighton. But Bloom said he would stick to a sensible spending strategy.
"The amounts of money in the Premier League does equalise things a bit," Bloom told the British media.
"We have to strengthen, that goes without saying. But we're not looking to spend huge amounts.
"We'll do things on a gradual basis as we have done. We have good players already, and we want to strengthen from that position."
Read the full article on eurosport.co.uk: Brighton chairman Bloom won't break the bank after promotion