The 31-year-old was pleased with how the team responded after back-to-back defeats, while keeper Ben Foster insisted they are not getting carried away despite rising to fifth place
West Brom striker Peter Odemwingie has admitted he may have handled the ball in the run up to his opening goal in the 2-0 win over Southampton.
The Baggies took the lead at the Hawthorns when the 31-year-old's shot deflected off Maya Yoshida past Paulo Gazzaniga, however replays suggested the attacker used his hand to control the ball in the build-up.
The Nigeria international did, however, indict that the three points were well deserved after battling back from recent disheartening display after conceding late winners against Newcastle and Manchester City.
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"Yeah, we needed a bit of luck," he replied to Sky Sports when asked about the handball. "It's simple, keep shooting and you will score. Sometimes they give penalties for the second, but we're happy with the three points.
"After two difficult weeks we played well and deserved at least a point from each game. But now, we kept our concentration until the last minute because we conceded lucky goals in the last minute. I think this is a good response of a good team."
Ben Foster had a quiet night on Monday, being forced into a couple of routine saves in the opening stages before one more demanding block from Adam Lallana late on.
The goalkeeper hailed his team-mates for their part in the win, while also praising the side for bouncing back from recent morale-depleting losses.
"Fantastic credit [to the team]," he added. "Like Peter says to bounce back from the two difficult weeks we've had. We were unlucky against [Manchester] City and that last minute one against Newcastle as well.
"I'm really happy to get the clean sheet, [we've] been conceding some really unlucky goal recently so [it's] great to get back to winning ways and a clean sheet too."
The 29-year-old was kicking the ball with his weaker right foot throughout the match after suffering an injury in training, but he insisted the damage is minimal.
He continued: " It's a bit swollen and I've had to get it taped up so I thought I'd give the wooden right leg a go tonight. It's fine."
The victory leaves Clarke's men fifth in the Premier League table with ten games played, however the former Birmingham keeper stressed the players are keeping their feet on the ground for now.
"It's a cliche but we're not getting carried away," he added. "We'll take each game as it comes and see where it goes.
"I think there's 14 odd teams hoping to get to that 40 point mark and take it from there and we're no different. We'll get to that mark as soon as possible and see what games we have left."