Ym mis Ionawr, fe bleidleisiodd y cyngor sir i ollwng y ffrwd Saesneg yn Ysgol Llangennech ger Llanelli.
Yn ystod y ddadl honno fe gyfeiriodd un cynghorydd Llafur at y penderfyniad fel "arwahanu" ac fel "apartheid ar ei waethaf", tra bod un ymgyrchydd blaenllaw wedi awgrymu y gallai pobl sy'n anhapus "groesi'r ffin".
Yn ystod sesiwn holi'r Prif Weinidog yn y Senedd, fe gyhuddodd arweinydd Plaid Cymru, Leanne Wood rhai aelodau Llafur o weithio gydag UKIP mewn ymgyrch yn erbyn y newidiadau.
Dywedodd Mr Jones: "Mae yna rai sylwadau sydd wedi cael eu gwneud gan wleidyddion nad wyf yn cytuno â nhw.
"Rwyf wedi gweld y sylwadau hynny ac yr wyf yn credu ei fod yn hynod o bwysig nawr bod pobl yn tawelu, a bod y gwenwyndra rydym wedi ei brofi yn lleihau."
"Lle Cyngor Sir Gaerfyrddin ydy hi i egluro'r penderfyniadau a wnaed ganddynt yn Llangennech."
Ychwanegodd Mr Jones fod Llywodraeth Cymru wedi ymrwymo i gyrraedd targed o 1m o siaradwyr Cymraeg.

The King Charles spaniel was found on the A38 near Kennford service station in Devon on Thursday afternoon.
The owners of the dog, which suffered two suspected broken legs, have now been traced.
CCTV footage is being reviewed  by police "to shed light" on the incident.
Devon and Cornwall Police said: "We are currently working under the impression that the dog had escaped from its home and ran across the road and sustained its injuries this way."

The South African struck 24 boundaries, sharing century partnerships with Luke Wright (60) and Ben Brown (67), as Sussex moved their score on from 74-1.
Jofra Archer then smashed four sixes and three fours to score 42 off 14 balls as Sussex declared on 443-6.
Leicestershire openers Paul Horton and Arun Harinath reached stumps unbeaten, leaving 389 runs to score on day four.
Mae'r Prif Weinidog wedi galw ar bobl i bwyllo yn y ffrae chwerw dros y penderfyniad i newid statws iaith ysgol gynradd yn Sir Gaerfyrddin.
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An injured dog which was first thought to have been thrown from a car on a busy dual carriageway had probably escaped from home and run across the road, police say.
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Sussex's Stiaan van Zyl scored an unbeaten 166 as Leicestershire ended day three 36-0 chasing 425 to win.