But despite that Les Bleus have won three from four in this year's Championship and with a win over Ireland, and a favourable result in Rome where Italy host England, Philippe Saint-Andre's side could yet be crowned champions.
And Szarzewski has moved to remind the French public that he and his teammates are striving hard to build a side for the 2015 World Cup.
"We are disappointed by the criticism, it's almost like certain people would prefer us to lose the games that we don't necessarily deserve to win," he said.
"Our goal is to be champions of the world and I would prefer the French people and public to get a bit more behind the team.
"Everyone wants to show a different side to our play to what we showed at Murrayfield.
"But you have to remember that it was a victory at the end of the day. Despite all the doubts we won the game and that is a good thing.
"The guys were a bit frustrated after the game, quite tired but from Monday everything starts again and we have had some quality training."
Szarzewski missed the clash at Murrayfield with an ankle injury sustained while on club duty with Racing Metro but is one of four changes for the match against Ireland.
Philippe Saint-Andre has also dropped Jules Plisson from his squad with Remi Tales in at fly-half while Gael Fickou starts at inside centre in place of Maxime Mermoz.
In the pack, Louis Picamoles is restored to the starting line-up in place of Sebastien Vahaamahina
"You never know how these things can play out but the swelling has gone down, I am feeling better," added Szarzewski.
"I have known some failures with the France squad (referring to Brice Mach's lineout struggles) I am here to help the France team and my teammates to improve."
FRANCE TEAM TO FACE IRELAND
15. Brice Dulin (Castres Olympique)
14. Yoann Huget (Stade Toulousain)
13. Mathieu Bastareaud (RC Toulon)
12. Gael Fickou (Stade Toulousain)
11. Maxime Medard (Stade Toulousain)
10. Remi Tales (Castres Olympique)
9. Maxime Machenaud (Racing Metro 92)
1. Thomas Domingo (ASM Clermont Auvergne)
2. Dimitri Szarzewski (Stade Francais Paris)
3. Nicolas Mas (Montpellier Herault Rugby)
4. Pascal Pape (Stade Français Paris)
5. Yoann Maestri (Stade Toulousain)
6. Louis Picamoles (Stade Toulousain)
7. Alexandre Lapandry (ASM Clermont Auvergne)
8. Damien Chouly (ASM Clermont Auvergne)
16. Guilhem Guirado (USA Perpignan Roussillon)
17. Vincent Debaty (ASM Clermont Auvergne)
18. Rabah Slimani (Stade Français Paris)
19. Alexandre Flanquart (Stade Français Paris)
20. Sebastien Vahaamahina (USA Perpignan Roussillon)
21. Wenceslas Lauret (Racing Metro 92)
22. Jean Marc Doussain (Stade Toulousain)
23. Maxime Mermoz (RC Toulon)
24. Brice Mach (Castres Olympique
25. Jules Plisson (Stade Français Paris)