"We made three offers, significant seven-figure sums," McNally told BBC Radio Norfolk.
"If we had our way he would have joined us and it would have been the biggest transfer fee this club has paid since January 2006."
That transaction was for Nottingham Forest's Robert Earnshaw, with the Canaries splashing out ?3.5m on the Wales international.
City boss Paul Lambert did most of his business early in the transfer window, bringing in
Leon Barnett,
Marc Tierney
and
Aaron Wilbraham
on permanent deals as well as securing Arsenal midfielder
Henri Lansbury on loan
until the end of the season.
Personally, I prefer that our club are doing their homework on players - it was the way the club gained most of its success in the 80s and 90s
Superman wears Grant Holt pyjamas
But McNally admitted that Bennett, who
handed in a transfer request
two weeks ago, "was the one that got away" as far as January's targets were concerned.
"This was a serious offer, we meant serious business," he added.
"Brighton are a great football club, good people, our relationship with them is unharmed by the events of the last four weeks.
"We can understand them not wanting to sell their best player, so we do have some sympathy but he was the one that got away."
Lambert will have the funds from the failed Bennett deal to use when the loan window opens next week.
But McNally insisted the Canaries, who are second in the Championship, would not be panic buying.
"We're not going to spend it for the sake of it," he said.
"In Paul Lambert we have a manager who is very good in the transfer market, he has the distinct quality of being able to spot a good footballer, which not everybody has.
"And we go into the rest of the season with the emergency loan market about to open in about seven days time and we've got money to spend if Paul wants it."
Source: BBC Sport
Source: BBC Sport