Defeat in the FA Cup at Hull City and a 4-0 home loss to Arsenal in the league followed, but Swansea rebounded to beat Liverpool 3-2 at Anfield, one of the shock results of the season, and followed that up with a 2-1 win over Southampton.
"It was a nice surprise," said Clement, whose team are 17th in the table, a point above the relegation zone. "Also because of the other managers who had very good results and teams this month.
"I was absolutely confident in my ability to do this job, and I haven't done the job. There's a long way to go."
Tottenham Hotspur midfielder Dele Alli won the monthly players' award after scoring five league goals in January.
Alli scored twice in Tottenham's 4-1 dismantling of Watford on New Year's Day, and followed that up three days later with both goals in a victory at White Hart Lane that snapped table-topping Chelsea's 13-match winning streak.
Alli, 20, got his final league goal of the month against Manchester City as Spurs came from two goals down to escape with a point from the Etihad Stadium.
Tottenham are currently second in the table trailing Chelsea by nine points.
"The team's done very well this month, not just me individually," Alli said. "We've had lots of players in form so it's an honour to win it."
(Reporting by Simon Jennings in Bengaluru; Editing by Toby Davis)
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