Adrian suffered the injury in the warm-up, but opted to play with West Ham already missing the likes of James Tomkins, Enner Valencia and Winston Reid due to injury.
The visitors' defence was breached late in the first half by Olivier Giroud's strike, before Aaron Ramsey and Mathieu Flamini made the points safe for Arsenal late on.
However, McDonald felt both Adrian and the rest of the team can take some positives from the defeat following a tricky run of fixtures.
"We've lost two [players] this week and even the goalkeeper has dislocated his finger before the game but played on," explained McDonald.
"He's dislocated his finger but said he wanted to carry on. It's obviously a big thing for a goalkeeper but he's been a brave lad today.
"We're disappointed at half-time, conceding right at the end, the team plan was always going to be to pass the ball a little bit better.
"We pushed them back a bit for the first half-hour but then got killed off at the end.
"He [manager Sam Allardyce] is trying to pick the players up, because they're really feeling sorry for themselves. He's obviously angry at conceding the two goals towards the end.
"He knows we can play better but playing against a team in the Champions League, after the teams we've played over the last few games and being without a few players, the players have given their all."
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