Steven Pienaar scored the only goal in the 16th minute but the hosts made harder work than they should have done in winning a 20th straight league match at home to Fulham.
"All we can do is try to win our games," said Moyes. "If we can do that and see how we do - we have beaten last year's total with those points today and that hopefully shows a sign of progress.
"We will try to keep it going until the end of the season and if we do get in Europe we will have certainly earned it because the sides above us are all good sides.
"People were saying we couldn't afford to lose any games. The important thing is to keep trying to win the next game.
"We've had to be looking at the other (team's) fixtures for a long time.
"If other teams keep winning their games there is not an awful lot we can do but if we win our games that is the big thing."