The Toffees remained sixth on the table after Phil Jagielka cancelled out Emmanuel Adebayor’s first-minute opener before Kevin Mirallas edged the visitors ahead at White Hart Lane.
However, Gylfi Sigurdsson snatched a late equaliser for Spurs but Moyes is not giving up hope of pushing towards a Champions League spot even though his side sits six points behind fourth-placed Tottenham.
"I don't know if a point does a great deal for us. If we'd won we'd have been right in it,” he said.
"I don't think we're too far away (from fourth) but I just hope the games don't run out.
“Tottenham are one of the top teams who have been fighting for fourth all season and we have taken four points off them this season so it is not a bad return.
"I'm pleased with a point because Spurs played well today. I thought we did as well, in patches.
"In truth, maybe we should have just about nicked it at the end.
"We don't have the squad to cope with that loss (of Marouane Fellaini and Steven Pienaar)."