Despite the fact that the Toffees were winning 2-1 until the 87th minute, they had benefited from the home team missing a number of chances, coupled with some saves by Tim Howard.
"One minute we were under pressure, the next we were breaking to score and it went that way through the second half. We were always a threat and scored a couple of good goals," Moyes told BBC Sport.
"Tottenham had a lot of chances themselves and we had to ride our luck at times without Marouane Fellaini and Steven Pienaar."
The result has left Everton sixth in the Premier League table.