Villa’s opener came from virtually the visitors’ first attack, while West Ham went on to have 17 shots, though they once again struggled to create many clear-cut openings.
“It should have been three points,” Zouma said. “We played a good game, we had many chances to score, but we couldn’t [finish them]. But that’s football, we got a point, we didn’t lose but obviously, we need to get wins.
“That was their only chance as well. The only chance they had in the box they scored, and they made the breakthrough. It is going to be hard until the end of the season, everyone can win but we believe in ourselves, we have the quality and we need to show it on the pitch.”
Zouma was making his first Premier League start since mid-January having returned from a hamstring injury against AEK Larnaca in Cyprus on Thursday.
It has been a disrupted season for the Frenchman, who also underwent knee surgery during the World Cup break. His fitness is likely to be key to West Ham’s survival hopes, as well as a push for glory in the Europa Conference League.
“I’m feeling good,” Zouma told the club website. “I’ve had a few injuries and it hasn’t been easy, but my family and the staff have helped me.
“I have been lucky because everyone has been behind me. I have managed to play two games in a row, two 90-minute games is very good, but I am ready to keep playing and keep going.”
Meanwhile, Moyes confirmed that full-back Vladimir Coufal is unlikely to be fit in time for Thursday’s last-16 second leg against Larnaca.
“He’s has got plantar fasciitis,” Moyes said. “He is improving. He is a boy who really wants to play. He’s desperate to get out and show what he can do but he’s got a foot injury. I don’t think he’ll be back this week. Maybe he could be back after the international break.”