Soft set-piece and individual mistake cost us - Wigan Athletic chief
Trying to arrest a 12-match winless sequence, Latics gave as good as they got for long periods at Sincil Bank.
They even took the lead through Kal Naismith's deflected striker eight minutes after the restart.
But after conceding a hugely contentious free-kick on the edge of their own box with 21 minutes remaining, Latics were pegged back by Jorge Grant's sublime set-piece.
And the visitors were denied even a point thanks to Tom Hopper's winning goal with seven minutes remaining.
"Obviously the over-riding emotion after the game is one of disappointment," Richardson said.
"But for large portions of the game, it was very pleasing.
"I thought we matched a very good side for large parts, we offered a threat with Kal Naismith coming back up front.
"Given the performance, do we deserve a result from that? I think we do, yes.
"We've been undone by a set-piece that was soft, and an individual mistake at the end.
"While we don't accept losing, we accept putting in a performance like that.
"Could anyone have given the shirt any more? No, I don't think they could."
Richardson was rewarded for pitching in Naismith after seven matches out injured.
"It's always a test when someone's been out for so long, and we've been missing so many players - senior players - for so many matches," acknowledged Richardson.
"It's a calculated decision as to when they can come back. and Kal thought he could give it a go and get through.
"He's played very well, he's scored a great goal, and he brought a lot to the team.
"Only the result dampens a very good performance.
"We're not hiding from the league position and the results we're having.
"We know there are other things going on around the club that have been spoken about a lot.
"All we can do is send lads out there who will do the shirt proud, and I think they're certainly doing that."