Stars suffered a humiliating 3-0 loss to derby rivals Bloemfontein Celtic on December 12, but have responded with wins over SuperSport United, Orlando Pirates, Bidvest Wits and most recently Cape Town City.
Eymael says it is important his team keep their feet on the ground after picking up some big scalps.
“Five [Ed: four] wins in a row, I don't know if it has happened here once and I don't know that statistic of that from the last years,” the Belgian said after the 1-0 defeat of City at Goble Park on Saturday.
“Secondly, is not like we only won against smaller teams. We also beat big teams Orlando Pirates, SuperSport United, Bidvest Wits and now Cape Town City, who has won trophies last season and they were fighting for the league title.”
Eymael, whose side next host a resurgent Maritzburg United this Saturday, added: “We will see what will happen. I want to thank my players, they fought a lot and showed big commitment.
“I want to thank the technical staff as well, we achieved this as a team. We will try to fight and try to stay humble and put our feet on the ground and we take one game at a time.
“Now our focus is against Maritzburg United, who got a nice win on Friday. We hope to have another good run against them.”
Maritzburg have risen to seventh in the Premiership standings after opening 2018 with a 2-1 win over Ajax Cape Town and 4-0 rout of Celtic.