Sylvain Distin hailed his Everton team-mates for keeping the faith after climbing to 11th place.
The Toffees were still without a win earlier this month and sat bottom of the Premier League with just three points from six games.
But victories over Birmingham and derby rivals Liverpool, and a 1-1 draw at Tottenham on Saturday, have propelled David Moyes' men up the table.
Distin is now hoping Everton can maintain that form, warning they could be back in trouble just as quickly.
"At the moment we're on a good run but two weeks ago everybody was saying the opposite," Distin told the club's official website.
"It's football - when things go wrong you have to keep working, but when things go well you have to do the same. In football it can change very quickly."
Everton took a 17th-minute lead at Tottenham through a Leighton Baines free-kick, only for Rafael van der Vaart to equalise three minutes later following a Tim Howard error.
Distin was disappointed to concede in such circumstances but the French defender feels the Toffees should be pleased to come away with a point against Spurs, who finished fourth last season and are currently fifth in the table.
"It was 1-1 with a goal we could have avoided, so I don't think we should be ashamed about our game," Distin added.
"The only downside was the way we conceded, but I'm still happy about the result altogether.
"We have to be realistic, we were away from home against a good team and I think it was a good result for us."