Dele Alli's injury-time strike appeared to seal a 3-1 victory for the hosts, but Valencia responded immediately to cut short Spurs celebrations and give the visitors slim hope.
However, Tottenham saw out a tense final few moments to secure a ninth consecutive Premier League home win and close to within seven points of top flight leaders Chelsea, who face West Ham at London Stadium on Monday.
And Koeman said Tottenham would have rightly felt hard done by if his side had snatched a point.
The Everton boss conceded: "We did some mistakes and if you make those kind, like the second and third goals, it was too easy," said Koeman.
"We did well. We had some good counterattacks but needed more composure on the ball. We had the chance to get a point but it was not deserved.