The home side trailed the Irish 23-3 at half time, but mounted a second-half fightback before losing 30-22 at the Millennium Stadium on Saturday.
While he was happy with his team's positive comeback, Biggar admits that the Welsh did not start anywhere near well enough.
"We have to start better. The first half wasn't good enough," he said. "We can only apologise for that, but that 10 minutes before half-time boosted us. It made us come out and play some good rugby in the second half, but we have to be more clinical.
"We were a little bit out of shape there.
"It's one of those things, but the way we bounced back after conceding points was a positive for us and something we have to take going forward."
The match was Biggar's Six Nations debut, and he will be hoping to retain his spot in the side when Wales face France in Paris on Saturday.