Had Sunderland been able to pick up a point against Everton, they would have made a big step towards safety as none of the other teams at the bottom of the table were able to win at the weekend.
Instead of capitalising, though, Fülöp admitted Sunderland were lucky not to be in even more trouble as a result of the deflating display against an injury-hit Everton side.
He said: “We were very lucky at the weekend again, but we can’t keep relying on that. We are better than that, and we need to start taking responsibility for our own position, rather than relying on other teams to do it for us.
“Our destiny is in our hands, but it is up to us to look after it, rather than depend on what is happening on another pitch. We need one more win. If we get that, hopefully we will be safe.
“This is all fairly new to me. It is the first time in my career I have been involved in something like this. But you have to be mentally tough and we have to get the points on board as soon as possible. We can’t always be looking out for other results.”
With just one home game against Chelsea to come, Sunderland will have to pick up points on the road against either Bolton or Portsmouth if they are going to keep their fate in their own hands.
Fülöp added: “We were all expecting a better season than this, and I accept that the fans will not have been happy with the last few games. But at least we still have our destiny in our own hands with three games left.
“I am sure Newcastle and Middlesbrough would swap positions with us straight away if you offered them the chance, and I am confident that we have what it takes to stay up.”
He continued: “It will be a very different game next weekend to Everton because Bolton will play a lot of long balls into our box, but we have got to cope with that challenge.
“We have been in the same position for a long time now and it is our own fault that we have not got enough points to improve it. Luckily, the opponents haven’t got enough points to really make a difference to our position.
“No one is happy with what happened at the weekend, but I suppose the only positive is that our position has not got worse because of it.”
