Chris Boyd's side suffered a 27-14 defeat to Leicester Tigers at Mattioli Woods Welford Road on Saturday, ending their chance to claim the league title.
It was tough to take for Saints as they created several good chances during the first period but only went in level at 6-6.
And skipper Ludlam said: "It's a tough pill to swallow really and you can't really put it into words.
"They were the better team on the day unfortunately.
"We can be proud of this group, and the way we've behaved in the past few months has been fantastic, and I couldn't be prouder of the boys.
"We wanted to be play again this week but it wasn't to be I suppose.
"The tough thing is that we had the chances and we just didn't finish them.
"When you get to the top end of the game, in knockout rugby, that's the difference - they took their chances and we didn't take ours.
"It's back to the drawing board.
"We'll use it as fire and motivation for next year.
"There's a lot of lads leaving but this group isn't done.
"We've just got to use this as fuel.
"We'll come back next season, use this and get better."