Wales were on the wrong end of a 30-17 defeat against England at Twickenham last weekend after handing their hosts a 17-point advantage before fighting back only to concede a late interception try.
And the 2008 Grand Slam winners endured a similarly sluggish start when they lost to Australia at the Millennium Stadium during the November series.
Those disappointments have prompted Byrne to remind his team-mates that they must be totally switched on right from the very first kick off and not just when the game appears out of reach.
"We know we have the talent but we only seem to start playing when we're losing," said Byrne, who started the first Test for the Lions against the Springboks last summer before injury brought his tour to a premature end.
"We must cut that out of our game because we can't keep giving teams that sort of advantage and then expect to win.
"There were a lot of positives about the way we came back at Twickenham. I thought we were going to pull it off, but we'd left ourselves too much to do.
"Instead of chasing the game, we have to be switched on from the kick-off. That's something we've lacked in the last few games."
Byrne also followed fellow Lion Shane Williams in refusing to blame Alun Wyn Jones for the opening-round defeat in London.
The Ospreys lock, who also toured with the Lions last summer, was yellow carded for tripping England hooker Dylan Hartley, with the hosts going on to score 17 unanswered points during his time in the sin bin.
But Byrne was keen to ensure Jones is not forced to take sole responsibility for the loss and, while he insisted that the team as a whole were below par, he still believes the Six Nations title is there for the taking.
"England really made the most of those ten minutes. I'm sure Alun regrets it now but it was an instinctive reaction," added Byrne.
"There were a lot of other mistakes so we can't point fingers.
"The boys have put it behind them and we'll pull together to bounce back on Saturday. We can still win the championship."