The Cottagers were 1-0 behind at half time before United ran rampant after the break, and Jol insists that his side were lucky not to concede more than four goals at Old Trafford.
Jol told Sky Sports News: "We tried to have good intentions and play our football but we couldn't. We couldn't link up from the back and we couldn't keep the ball.
"It was still 1-0 at half time so we were still in it, but we came out and they scored two early goals and the game was finished.
"Luckily enough they only scored a fourth goal because it could have been one of those days that they scored six or seven."
Fulham's defeat was their second in Manchester in the space of a week after they fell to a 2-0 defeat at the hands of Manchester City last weekend.