The ex-Eagles captain admits he had feared for the club but believes the international break has benefited them.
The Eagles have suffered a terrible loss of form since Christmas which has seen them fail to win any of their last 14 league matches, losing nine of those fixtures.
That slump has caused them to fall from a place in the top half and being touted as an outside candidate for European qualification to just seven points outside the relegation zone in 16th.
However, Alan Pardew's side showed spirit to fight back and draw 2-2 with European challengers West Ham United at Upton Park in their first game back after the international break, and Thomas believes they have enough quality to avoid any true danger.
The 51-year-old, who played 249 times for the club and captained them to the 1990 FA Cup final, told the Croydon Advertiser: "Palace have got enough quality to stay up. I said to someone back in November there's always a side who drops down or loses form [and] I was slightly fearful of Palace being that side because everything seemed to be going too well at the time.
"They had a couple of bad results and I wanted to see how they reacted. They have been on this bad run but will turn it around – they have to turn it around. Getting to 40 points is doable very quickly and let's see where they end up.
"I think it the international break was a good time for Palace and for some of the players to go away with their countries. It has given everyone a chance to re-evaluate everything and have a fresh start towards the run-in."
Palace have the perfect chance to take a huge stride towards effectively being safe if they can beat 17th-place Norwich City in their next match at Selhurst Park next weekend, knowing that a victory would put six points between themselves and the Canaries regardless of the results of other struggling teams.
If they were to come away with all three points from that encounter it would be their first league win since 19 December, and that could be a crucial match for them with league games against Arsenal, Everton, and Manchester United on the horizon before their FA Cup semi-final against Watford on 24 April.