The former prime minister stressed that the reaction to the stabbing of the Southend West MP could not allow “democracy to be diminished”.
Sir David was attacked on Friday morning in his constituency.
Mr Brown also demanded MPs be given better police protection, and said he expected measures to be introduced within days.
Speaking to Sky News, he said: “This is an attack on our democracy, so the answer cannot be less democracy.
“This looks as if it is a terrorist incident, it is probably related to Al Shabaab or to al Qaeda, and we’ll find out more in the next few days.
“But the answer when you come across a terrorist incident is we don’t blink, we don’t shirk, we don’t flinch, we don’t show weakness and we stand up for what we believe.
“And, of course, we will increase the security that is available to Members of Parliament and councillors when they’re doing their surgeries, and that is something that must happen immediately.
“But it’s true also to say that we must not allow our democracy to be diminished because a terrorist attack has occurred.”
The Labour stalwart also warned the country must show “no weakness”.He continued: “I think the history of dealing with terrorism is that if you ever show weakness and if you ever give the impression that coexistence is impossible and that you’re going to back away and give up on your values, then you show something that gives terrorists hope.
“We must not do that.
“Hearts are broken, but our resolve must be unbreakable.
“A life has been tragically destroyed but our values – our democratic values – they are indestructible, and we must show that now.”
Mr Brown also called for police protection to be available.
He added: “It need not be obtrusive, it need not be so obvious, but I think the protection has got to be made available now to Members of Parliament who feel that there is a risk to what they are doing.
“I think that will be introduced in the next few days.”