Chasing back-to-back wins for the first time in club history, the Suns led the defending premier by a point at quarter-time and stayed with the Sydney Swans for most of the match.
However, the home side pounced on some costly turnovers and showed a touch of class to outlast the Suns and remain undefeated with a 41-point win.
"Mentally I thought our boys really stood up to the line and really had a crack," McKenna said.
"It could have been better no doubt but certainly the effort was there.
"We just need to consistently provide that and if we do we give ourselves a chance of winning like we did last week."
McKenna said the fact his side was able stay with the Sydney Swans for much of the match despite a quiet day from skipper Gary Ablett, who finished with 24 touches, showed that some of the other members of the team were stepping up.
"Sydney aren't a team of champions, they are a champion team and together they certainly put the clamps on Gaz," McKenna said.
"But I can't fault the skipper's ability to work and try and put some of our other players into space."
While conceding 17 goals in a game is far from ideal, McKenna said the Suns' backmen "held up fairly well".
"It wasn't so much the poor defensive mechanisms it was just more our turnovers and our quality going forward," McKenna said.
"I'm very comfortable out of a strong defence will come a really good offence.
"We just need a bit of composure."
