Chelsea kept alive their hopes of finishing in the top four after an early goal from Cesc Fabregas helped them secure a 1-0 win over a Swansea team who are just one point above the bottom three and face a major battle to retain their top flight status.
Chelsea faced some level of discomfort due to Swansea's late push for a point and the match produced even more drama when Nathan Dyer tumbled to the ground inside Chelsea's penalty area on the wake of a robust challenge from Gary Cahill.
Chelsea went close to doubling their lead once more in the 74th minute, as Fabregas picked out Victor Moses at the near post but the wing-back was unable to convert as the ball squeezed wide of the post.
"Every game we have to show our pride and show we want to make it happen, put pressure on the teams above us", he said. They play against Watford on Monday but in football it is not simple to win the game, especially in this league.
The Spaniard scored the only goal of the game with a splendid finish after Eden Hazard caught the eye with his artistry in the build-up to the same. "The big problem we are having this season is that we create many chances to score but we don't take them", Conte said.
Southampton could yet have the chance to overtake Swansea when they visit the Liberty on Tuesday, 8 May before Stoke travel across the border on the final day of the season. "I think this season we are not clinical and in the last period we are winning but also playing a little bit where we could kill the game but don't".
"When I arrived we were five points to the teams above, we depended on others to try and get out of this position", he said.
Swansea's gap to the relegation zone was cut to one point after Southampton's 2-1 home victory over Bournemouth - and it is now six games without a without a win for Carlos Carvalhal's side.
"We're just doing everything we can at our end".
"It was a hard game, emblematic of the whole season", Cologne coach Stefan Ruthenbeck said.
Matt Phillips gave West Brom a glimmer of hope in their fight for Premier League survival as they won 1-0 at Newcastle to extend their unbeaten run to four games.
"We are still in an important situation but we have to maintain this level of performance in the next three games".