Second-half goals from returning striker Alvaro Morata and compatriot Marcos Alonso earned Chelsea three points in the Premier League on Tuesday, their headers breaching Brighton and Hove Albion's disciplined defence after a fallow first half.
Chelsea, spearheaded by the lively Eden Hazard, enjoyed the lion's share of possession with nine first half shots, but Tiemoue Bakayoko, Victor Moses and Cesc Fabregas all wasted chances.
Goal scorer Morata, back after suspension for Saturday's 0-0 draw at Everton, sprang to meet Cesar Azpilicueta's diagonal ball in the 46th minute and Alonso's near-post glancing header from a corner by a fourth Spain international, Fabregas, made it two 11 minutes later.
The win increased pressure on second-placed Manchester United who could only manage a 2-2 home draw with Burnley.
Conte said there was "great motivation, to try to stay there, to try to fight until the end" but said the challenge to overhaul Manchester City's 13-point advantage over Chelsea - having played a game less than the Londoners - looked too great.
"We fight for a place in the Champions League next season. There are four places for six top teams," he said.