The Cottagers went ahead through a superb Giorgos Karagounis strike, but failed to capitalise on their lead before Franco Di Santo equalised for the Latics.
But, despite expressing disappointment with the result, the 28-year-old believes Martin Jol's men must "move on" as quickly as possible.
"It was obviously a frustrating afternoon," Kieran told the club's official website. "I thought we’d won it at the end when their defender cleared it off the line from Bryan’s shot, but it wasn't meant to be.
"Their goal was a great strike but we've got to take the point and move on. They got the goal and then they had a 10 minute spell where they kept the ball well and were on top in the game.
"We weren't keeping the ball as well as we know we can but that happens in football. There’s no point letting our heads drop, we've got to pick ourselves up. We can’t dwell on it and we've just got to move on."
The Manchester United youth product has recently been deployed at left-back for Fulham, but insists he is happy to play anywhere on the pitch for the good of the team.
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"It’s not a new position to me – I've played the last few seasons there,” he explained. “I’m very comfortable at left-back and I enjoy it. Obviously on Saturday I didn't get the ball as much as I could because as a defender you’re mainly defending – that’s the priority.
"Defending is the most important thing but you've got to get forward as well and, with the players we've got, we keep the ball well so there are a lot of opportunities to get forward.
"I was happy with my performance, especially in the second half when I got tighter to their wing-back [Emmerson Boyce]. I was happy to get another 90 minutes for the club. My fitness is coming and, hopefully, I’ll be in the game for Blackpool."
Fulham face a midweek trip to Bloomfield Road to take on Blackpool in an FA Cup third round replay, and Richardson is expecting a tough game against the Championship side.
"I've been there before and it’s a hard place to go but we can’t blame the pitch,” he said. “We've just got to get on with it. We've got to be professional and go there and try and do a job.
"They’ll be up for it because it’s the FA Cup but we’ll go there and I’m sure we’ll do the business.
"It’d be great to go through. United have got West Ham at home [in a Replay on Wednesday] and they should win that but you never know in the FA Cup. Whoever we get I’m sure it’ll be a hard game for us, but we’ll try our best to make sure we are there to challenge."