Mandzukic converted from the penalty spot in the first-half, after Diego Godin was brought down by Granada’s Abdoul Sissoko in the box.
Garcia, who replaced the Croatian striker as a substitute in the closing stages, sealed the three points when he headed home from Arda Turan’s floated cross.
And the manager believes the title race will go down to the wire.
‘You’re seeing a very close race in La Liga. There are teams fight for third place like Sevilla, Valencia, Villarreal…’ Simeone said.
‘We expect to work hard and we must continue to maintain the same desire and intensity. The second half of the season is always more difficult because everything is up for grabs and the teams all play a certain way.
‘Granada were very organised defensively and we progressively improved as the game wore on.
After the 25th minute, we improved. Mandzukic and [Fernando] Torres are two players with different characteristics and I’m happy with their performance today.’
And the Argentina reserved special praise for Arda Turan.
‘Arda is at a point where he knows he’s a game-changer and the team needs him,’ he added. ‘In the time he’s been with us, he’s grown defensively. He has natural-born talent.’