Costa played the full 90 minutes on Wednesday as Chelsea eased to a 3-1 victory over Sporting Lisbon in the UEFA Champions League.
The Spain international has featured in four games without scoring since claiming his 11th Premier League goal of the season against West Brom on November 22.
Yet Mourinho declared himself pleased with the 26-year-old's contribution in the clash with Sporting, as Costa seeks to return to peak fitness and form after persistent hamstring trouble this term.
"He wants to improve his condition," explained Mourinho. "The confidence is not high, the condition is not the best but he wants to use the game [against Sporting] to chase lots of runs and movements, always wanting the ball, always wanting to associate with the wingers and with [Cesc] Fabregas.
"[It was] very important for him. I saw him better than against Newcastle, better than against Sunderland. This game was important for him."
A Papiss Cisse brace at St James' Park ensured Chelsea tasted defeat for the first time in 24 matches, but they remain top of the Premier League - three points clear of reigning champions Manchester City - and will be expected to get back on track against a Hull side that is winless in eight.
Steve Bruce's men dropped into the bottom three following a 0-0 draw with West Brom in their last outing and have three fewer points at this stage of the season than they had in 2009-10, when they were ultimately relegated from the Premier League.
Bruce could hand a recall to captain Curtis Davies, who has been left on the bench for his side's last two matches, and Nikica Jelavic will hope to start after illness restricted him to a late appearance as a substitute against West Brom.
