The offer for Bissouma, thought to be worth around £25million, was rejected by the Seagulls, who valued the Mali international at close to double that amount.
Gerrard had been keen to add a defensive-minded midfielder during the January window following the serious injury sustained by Marvelous Nakamba.
Yet it proved to be the only disappointment of a month the Villa boss described on Tuesday as “extremely strong”. Villa also held talks with Juventus midfielder Rodrigo Bentancur, who eventually moved to Tottenham.
Gerrard said: “In terms of incomings, the window was extremely strong. There were areas that we needed to find solutions for us to be stronger and better. We got 90 to 95 per cent of business done we wanted and I’m delighted with the support from the board.
“It was well documented that we put in a bid for Bissouma at Brighton which was turned away, and we respected and appreciated.
“If a move is not right then we will not become desperate and make decisions we do not think are right. If it’s not right at the time, we might have to be patient.”
Gerrard, who recruited playmaker Philippe Coutinho, defenders Lucas Digne and Calum Chambers and goalkeeper Robin Olsen during his first window as boss, is likely to revisit the midfielder search in the summer.
He continued: “Pre-window and during the window we were probably linked with 12 holding midfielders. It’s a position we’re looking to add in. Going into last month with the injury to Naka I felt it was a priority to try to solve it, but we’ll only make decisions and say yes to certain situations if they’re going to be right for Aston Villa, if they’re going to improve the team and squad.
“I won’t be a manager who will try to be wasteful or compromise in certain situations and go down the list, because I believe our fans and this club deserves the right people in the right positions.
“The support I’ve had during the first window and since I walked in the door has been brilliant and I really appreciate that.
“We will keep analysing the squad and if we feel we need support in that area we’ll look for the right target. We won’t compromise and try to find Plan B, C, D or E. We’ll keep pushing and try to get the right person.”