The German manager said his players were tired and unhappy, badly needing a break as they slip in the Premier League table, goal.com reported.
Chelsea, once in contention for the title, are now 12 points behind Manchester City with one more match played.
"[Even] in the reaction of the goal [we scored], you can see that we are tired," Tuchel told BT Sport. "We are relieved but there is no joy.
"We look tired, and we are. ... You can see we are mentally tired. We need some days off, there's no other solution."
On Romelu Lukaku and Hakim Ziyech being seen arguing at half-time, he said: "It's normal that they [Ziyech & Lukaku] talk, it's normal that they're not happy."
Ziyech opened the scoring for Chelsea in the 28th minute, but Brighton's Adam Webster headed his side level in the second half to secure a point.
"Chelsea are struggling a bit, we sensed that," said Webster to BBC Match of the Day. "We felt we could have got all three points but in the end are happy with the draw."
Chelsea have now failed to win any of their last four Premier League games in which they have scored first, the same number as in their previous 26 such games.
And after four clean sheets in five games, Chelsea have only kept four clean sheets across their last 16 matches in all competitions.
Neither the on-field play nor the off-field mood has been satisfactory for the Blues of late, with a feud between Tuchel and striker Lukaku hanging over a dismal run of results.
Next up for Chelsea is Tottenham on Sunday.