But at one point in November a slump in form saw the Edinburgh outfit sit just two points from bottom of the Scottish Premier League.
"We were really worried about relegation at one stage. It was a genuine concern," he said.
The best home defensive record in the league has gone some way to lifting the Tynecastle side up the league, with another narrow victory on Saturday taking them closer to their city rivals.
"We were trying to get a second goal to make it easier for us and I had a chance but cut in and just misfired my shot," added Obua.
"But the most important thing was that we won the game and got three more points in the league.
"I told the club at the start of December which players I would like, but there is no news yet
Hearts manager Csaba Laszlo
"Whenever you win you are happy because even if it's just 1-0 that's all you need to do. We got our goal and then we played well in defence after that.
"The fans were a bit anxious at the end which is understandable but you just have to block that out of your mind and keep on playing to make sure you get the right result."
Obua admitted the team would benefit from the addition of a couple of experienced players during the January transfer window, but that prospect appears increasingly unlikely.
Hearts manager Csaba Laszlo said: "I told the club at the start of December which players I would like, but there is no news yet.
"We still have two weeks to bring someone in and I hope that is the case."
Source: BBC Sport
Source: BBC Sport