McClenaghan was poleaxed during the Black Caps' win over Pakistan in Wellington on Monday when an Anwar Ali delivery smashed through his helmet grille, fracturing his left eye socket.
The injury revived painful memories of Australian batsman Phillip Hughes' death after a ball struck his head in 2014, with Boult saying he did not want to dwell on McClenaghan's injury.
1st ODI: New Zealand win against Pakistan by 70 runs
"It's never a nice sight to see one of your team-mates down on the ground, it's pretty scary, (but) it's just part of the game, it's been going on for years," he told reporters.
"It's just a shame it happened yesterday.
"It still churns your stomach a little bit to see stuff like that happen and it's hard to talk about to be honest but we've jut got to move on, it's just part of the game and it's always going to happen."
Boult said modern helmets did not allow the ball to pierce the grille, but McClenaghan was wearing older style headgear with a slightly larger gap.
McClenaghan retired hurt and will not take part in the rest of the three-match series against Pakistan.
New Zealand won the opening one-dayer by 70 runs and the second ODI will be held in Napier on Thursday.
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