Despite the gap, with Atletico Madrid sandwiched in between the pair in second place, Solari insists his players will continue to fight for the title until it is mathematically out of their reach.
"We are fighting in three competitions until the last, as always," he said. "For Real Madrid, nothing is impossible.
"I always enjoy football and the competition, it is our passion and we love it despite the tough times. We are passionate about competing and obviously it is better to win, no one can deny that."
2 - Real Madrid’s Modric, has scored in back to back LaLiga games for the first time after 284 league appearances. Fire. pic.twitter.com/N3WOWEioX2— OptaJose (@OptaJose) January 19, 2019
Sevilla had the best chance in the first half at the Santiago Bernabeu, Sergio Escudero failing to finish off a flowing move on the counter as he shot into the side-netting with his left foot.
However, Madrid were by far the better team after the break, eventually taking the lead through Casemiro's long-range strike in the 78th minute before the excellent Modric added another in stoppage time.
"It's always more than just the three points when you're up against a direct rival, because one team gets the points and the other loses them," Solari told the media.
"The celebration was worthy of Casemiro's wonderful goal, and it was tense because I couldn't see if it was going in or not. It was a fantastic effort, not only because of the significance of the game, but because we needed that breakthrough."
On Modric, who played on despite suffering a cut in the first half following an aerial collision with Sevilla's Franco Vazquez, the Madrid boss added: "He was outstanding. Considering he had big gash that they had to stitch up.
"He's a fighter, he played a wonderful second half, split his eyebrow, then after 15 minutes [at half-time] they patched him up, he came and got the goal at the end. That speaks volumes about the spirit in this team. It was a very complete performance."