Chairman Tony Bloom has welcomed Brighton's "many excellent signings" but admitted disappointment at failing to sign another striker.
The Premier League new-boys were busy in the summer window, bringing in 11 players in total, but boss Chris Hughton was after an out-and-out goalscorer to improve his options further.
Albion were heavily linked with Raphael Dwamena but they failed to land the FC Zurich forward on deadline day, while Porto striker Moussa Marega and Spurs' Vincent Janssen were other late targets.
Bloom was pleased with the majority of the transfer business the club conducted but conceded the lack of a new striker is a worry.
In an open letter to supporters on the club website, he said: "We have secured many excellent signings which have strengthened the squad in many areas. In doing so, we have invested many tens of millions of pounds and we have broken our own record transfer fee three times.
"However, in what turned out to be a very eventful final day, we failed to secure the additional striker which has left all of us feeling very disappointed.
"Our recruitment team, led by Paul Winstanley, worked tirelessly throughout the summer - and indeed in the many months before - to identify targets, prepare the ground work for our transfers, and to put us in the best possible position to execute deals at the optimum time in the window. A far from easy task, and a far from exact science."
The letter went on: "Transfer windows are highly complex and dynamic. They require considerable investments in time, resources, energy, judgement, and, of course, finances.
"We were short in none of these areas. Transfer windows also require patience and good fortune. We were patient from the outset but, in the end, fortune did not come our way."