The Stamford Bridge outfit have struggled to return goals from their strikers, with Samuel Eto'o, Fernando Torres and Demba Ba managing to strike just five times between them this term.
It was a similar story in Chelsea's 1-0 triumph over Swansea City on Boxing Day, with Eden Hazard's strike settling the game, while Eto'o had opportunities either side of half-time to get on the scoresheet.
On both occasions he was foiled by goalkeeper Gerhard Tremmel, the German making a particularly fine stop just after the break.
Mourinho does not fault his forwards for their efforts, but has challenged his frontline to improve their goal return in the second half of the campaign.
"They kill me. Every game I'm tired in the end," he said.
"If in the second period (of the season) instead of five, they score 10, we have more chances (to win the title).
"They always give something to the team. Every one of them that plays. No goals, no winning goals. Okay, but they give what they can."
Chelsea - who occupy third in the Premier League table - continue their assault on the title in Sunday's showdown with fellow high-flyers Liverpool.
