January signing Nikica Jelavic scored the only goal in the 1-0 win over Tottenham as the Toffees prepare for a derby meeting with Liverpool in the Barclays Premier League on Tuesday and an FA Cup quarter-final with Sunderland next weekend.
Everton made it 10 matches unbeaten and dented Tottenham's hopes of holding on to third in the table, leaving Moyes looking forward to the week ahead.
He said: "It's a hard week for us but it's the sort of games I want to be involved in."
Moyes, who celebrates 10 years at the club this week, added on ESPN: "I have always hoped when I came here that we would be able to challenge with the big teams. We were a bit lucky but we got three points."
Moyes also praised Jelavic whose chances at Everton have been hampered by injury and the international break since he moved to the club from Rangers.
He said: "I thought he played well and took his chance really well."
Tottenham manager Harry Redknapp could not believe his side had failed to score after seeing Jermain Defoe have a goal ruled out for offside and substitute Louis Saha shoot against the post late on against his former side.
Redknapp said: "How did we lose it? In the second half we never came out of their half. We just couldn't get a goal.
"They couldn't get the ball off us. We penned them in and we just couldn't get the break.
"It was just one of those days in the end."