The Irons won 3-1, with Areola outstanding in goal for the visitors.
Moyes said, "Alphonse's goalkeeping and his saves have been great.
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"You could hear the crowd here chanting his name here today and quite rightly so. He deserves all the plaudits he's been given.
"He played brilliantly well, saved a good penalty kick and we move onto European football again in midweek with a bit of confidence again.
"We've won away from home, that's back-to-back wins in the Premier League and we've come through a bit of a sticky patch in January and the start of February.
"Hopefully we're beginning to see the light a little bit, so let's keep the form up."