The opening weekend of the new Premier League season has seen a glut of goals, but neither Swansea nor Southampton could register in the clash at St Mary's.
Clement has conceded that Swansea had "a tough afternoon", and the 45-year-old is glad that his team managed to secure a point after struggling against the Saints.
"It was a hard afternoon, they had a massive amount of chances, set play after set play and we suffered at times. I'm happy we ended up with a point and it could have been a lot worse. The last-gasp defending was good but we didn't use the ball well enough further up the pitch," Clement told BBC Sport.
"We are pleased we have got out of here with a draw. Every game we play we have to try to get points on the board and look to play better. I'm sure they will be disappointed and think 'how have we not won'."
Next up for Swansea is a home game against Manchester United on August 19.