The 34-year-old, who won 100 caps for New Zealand, was captain of the Irish province for the first time with regular skipper John Muldoon among the replacements.
Connacht had to weather a storm in France, battling back from a 20-11 half-time deficit to claim a bonus point in a 30-20 victory.
And Muliaina, who made his GUINNESS PRO12 debut in November, saw shades of the reigning world champions in his current club side.
"It shows a lot of character and real belief within the Connacht guys," Muliaina told stuff.co.nz.
"You can't train a lot of that. It shows the will to have your mates' backs, dig deep, and make sure your lines are not breached.
"There were times when I was thinking 'oh man, I have been in All Black sides when things weren't going well, when you haven't had your hands on the ball, the clock is ticking, and all of a sudden you have lost the game'.
"There certainly was a little bit of that again, but fortunately we had a couple of X-factor players who finished the job.
"But there is another thing, one I never thought about with the All Blacks, and that is a growing belief in this squad that we can win close games and close them out, and we did that."
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