The Hammers are taking part in their first ever group stage campaign in Europe and got off to the perfect start in Croatia when Michail Antonio took advantage of a mistake to round the Dinamo Zagreb goalkeeper and make it 1-0 just 21 minutes in.
Moyes saw his men dominate the opening exchanges in the game and made it 2-0 in the 50th minute when Declan Rice struck.
Rice finished well with a powerfully hit shot which went through the Dinamo Zagreb goalkeeper’s legs.
It finished 2-0, handing West Ham all three points and a good start to their Europa League campaign.
Moyes is delighted with how his side performed and admits he does not quite know just how good West Ham can be.
The Hammers boss insists he is looking to make sure the fans have European football to watch into next year.
“We are learning. I am excited at the prospect of not knowing how good we could be”, Moyes told his post match press conference.
“We made changes and we did not look any worse for it.
“My target is to make sure we have European football after Christmas.
“But it is only one game and we have to try and continue the level we are at.”
Moyes also had words of praise for Rice, who he believes had a superb European night for the Hammers.
“What he has tried to do is take himself to the next level. He is a terrific player who is getting better.
“He was the captain of West Ham in Europe away from home and he scored a goal.
“You must not forget he is 22 years old, a young boy with a big future”, he added.
The other game in Group H saw Belgian side Genk edge out Rapid Vienna 1-0 in Austria.
