The coach was disappointed with the Biancocelesti's performance on his return to the Stadio Olimpico hotseat, but thought they silenced Walter Mazzarri's high-flying side well
Reja, who was confirmed as Vladimir Petkovic's replacement on Saturday, marked the start of his second stint at the Stadio Olimpico with a victory thanks to Miroslav Klose's 81st-minute winner.
Despite securing three points, Reja claimed his side can improve much more under him.
"We haven't played very well today. We can do much, much more," he told Sky Sport Italia. "These three points give us some peace of mind, but we know we are not in the best condition."
The victory keeps Lazio in the top half of the table, in 10th, while Inter sit in sixth after Verona's win over Udinese earlier on Monday.
Despite his reservations over the Biancocelesti's showing, Reja was pleased to secure the win against one of the league's better sides.
"Inter are a very good team and can take advantage of any errors you make, especially if you give them space out wide and in midfield," he added.
"I thought we played a smart game today though."