The Welsh international's interception pass gave Leinster wing Isa Nacewa the chance to score what turned out to be a crucial first-half try.
But Biggar, who scored all his side's points against Leinster, says he and his team-mates deserve to be acknowledged for the manner of their performances.
He said: It's been all about belief, this trip. We've had a blow on Saturday afternoon and the boys have really dug in and I think this week has maybe answered a few critics about being mentally tough or whatever papers and things have been writing.
"It's shown how strong and tight-knit a group we are and a drop-kick or interception pass either way and we could have won three out of three.
"So it's a massive, massive plus for the boys to show the character we did this week."
Scrum V analysis: Leinster 20-16 Ospreys
Leinster moved seven points clear of the Ospreys at the top of the Magners League after winning the battle of the top two at the RDS.
But the Welsh region remain strongly in the hunt for a play-off spot although they also face a Celtic League disciplinary hearing into the postponement of the game at Ulster that was due to take place in March.
The Ospreys could be docked points over that issue and it left them facing the three-games-in-six-days schedule.
Biggar said: "It's been challenging, something new for the boys - they probably haven't done it before, three games in six days.
"But that's the hand we were dealt this week. But the boys battled in and really put in a superb effort with a bonus point win on Tuesday night after the bitter disappointment of Saturday.
"And we got what could turn out to be a precious point against Leinster, the home of the champions of Europe.
"It's been tough, but overall it's been an extremely positive experience.
If we can get a home semi in the play-offs we'll fancy ourselves
Dan Biggar
"It's going to be difficult, playing three games in six days, but we're not using that as an excuse for not winning in Dublin.
"We should have got over the line, going in at 16-10 ahead at half-time.
"Unfortunately we weren't quite able to, but it could turn out to be a very important point come a few weeks time.
"If we can get a home semi in the play-offs we'll fancy ourselves."
The Ospreys remaining fixtures are at Munster before they host Newport Gwent Dragons.
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