BBC Football Scotland
Christophe Berra secured victory at Hampden with an 85th-minute header.
"I thought it was important to win, really important, " Strachan said. "Just to make us feel good about ourselves.
"The performance at times was good as well, comfortable, brave on the ball, patient at times, getting used to the new pitch as well. It's a bit slick."
Scotland dominated possession at Hampden but were frustrated by Hamilton goalkeeper Michael McGovern in a lively first half.
The game threatened to peter out in a second half punctuated by a steady stream of substitutions, until defender Berra headed home debutant Matt Ritchie's corner.
Strachan was particularly pleased that neither Scotland goalkeeper Craig Gordon nor half-time replacement Allan McGregor had a save to make.
"Northern Ireland have improved immensely over the last year; beating Hungary, Greece and the Faroe Islands, " he said.
"I thought the first half-hour was a good start for a friendly. It was a good attitude, I'm pleased with the number of chances and the way we made them.
"And I'm delighted with the number of chances that they didn't get. There wasn't many chances."
Scotland are third in their Euro 2016 qualifying group, three points adrift of leaders Poland.
Strachan acknowledged there were "one or two things" his side could improve on against Gibraltar, who are bottom and have conceded 21 goals in their four qualifying games so far.
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