Thierry Henry's injury-hit side were taken apart at Stade Louis II on Sunday as Edinson Cavani's hat-trick inspired a 13th straight league victory for PSG.
Tuchel's men had already set a record for the longest winning streak at the start of the season in any of Europe's top-five leagues.
With five points from four games leaving PSG third in a congested Group C of the Champions League, progression into the knockout rounds is far from certain.
And Tuchel yearns for improved performances in Ligue 1 even though his side demolished Henry's struggling Monaco.
"I am very happy with the result and the fact that we went for a 13th victory in a row. It's extraordinary," Tuchel told a news conference.
"On the other hand I was a little disappointed with our intensity, our structure, and the quality in the first half.
"It was OK but we relaxed from the last games where we had a lot of pressure. After the first two goals we lacked structure and intensity.
"Monaco could have scored one or two goals. In the second half we were more serious. The result is great but it could have been better."
3 - Edinson Cavani is the first Paris' player to score at least three goals in a same game against Monaco in Ligue 1 since Carlos Bianchi on 25 May 1979. SouthAmerica. #ASMPSG @PSG_English pic.twitter.com/z73RWwrhx8— OptaJean (@OptaJean) November 11, 2018
Cavani missed PSG's last two league games with a thigh injury but the Uruguay international returned to the team in style by taking his tally to eight Ligue 1 goals this season.
The striker, who scored the first league hat-trick by a PSG player against Monaco since Carlos Bianchi in 1979, suggested the match was tougher than the comfortable scoreline indicated.
"It was not easy. It's easy to say that it was after the match," Cavani said to Canal+.
"We know that Monaco are not going through a good time. Their motivation is to try to get out of this situation.
"We scored at important moments, which allowed us to win the match."