Wilfried Bony's brace saw off Leicester at the Liberty Stadium.
"It was about getting three points as we could feel that little bit of pressure on us within the crowd and amongst the players," Monk said.
"It was never going to be easy, especially when Leicester threw caution to the wind, and we could have controlled the ball a bit better in the second half, but I thought we deserved it.
"We limited them to shots from distance which is credit to the shape we've been working on and how hard defensively we've been working.
"Three goals we've conceded in the last two games - two against Newcastle and the second one against Stoke - has not been the standard we've set but we got back to that to keep a clean sheet."
For the big stories and the banter follow us on Twitter: @tribalfootball