The former champions were under the cosh for most part of the match.
Eguma also had to line-up a squad without eight of his key players.
Chidi Osuchukwu, Abduljeleel Ajagun, Chizoba Amaefule, Emem Eduok, Isiaka Olawale, Chimaobi Chukwu, Emeka Atuloma and Victor Ezuruike were all missing owing to international assignment, injuries and personal issues.
Eguma said his team "showed determination" to earn a 1-1 draw at the Kwara State Stadium against Kwara United.
“I must give it to the boys. They gave their all and showed determination even as we all know that a lot of key players were out.
“I had to encourage them and tell them to go for it and I’m glad that they showed the stuff they were made of,” Eguma said.
Eguma had to name the trio of Baker Ebiabowei, Jimoh Ismail and Tope Jaiyeola in his starting line-up in the absence of his regulars.
The match statistics clearly showed that Dolphins were second best but the away point proved valuable for the Pride of Rivers.
Former Rising Stars forward, Yahaya Adamu put Kwara United in front in the 39th minute.
Fred Okwara scored the equaliser from a rebound with a quarter of an hour left in the game after Kwara United goalkeeper, Kazeem Yekeen spilled Osita Echendu's shot into his path.
Dolphins now have 18 points while Kwara United have a point more than their Port Harcourt opponents.