I can't find details of any debate on the Erasmus/Horizon question, only remarks made in support of the amendment.
Maybe someone more experienced in the intricacies of Hansard can help.
Being "open to participation in the next Erasmus+ programme" is a vague, empty phrase. It certainly does not suggest that the issue is seen as important or worth fighting for.
This vote doesn't mean the UK is out of Erasmus+, but if the amendment had passed it would have sent a message that the UK was keen to remain in it. Kicking the can down the road and including the question in the negotiations (which is probably viewed by some as a canny poker move) prolongs existing uncertainty and means that many EU universities will now encourage students to look elsewhere for mobility in the 2020-21 academic year.
Current contracts run until the end of 2020; we don't know whether the UK will be in beyond that. Outgoing UK students won't be able to apply for mobility programmes in the EU post-2020, as application will happen during the negotiation period. MFL students, who often do a semester in one country and the second in another as an integral part of their degree course, will be penalised.
The continued risk of No Deal and the UK gvmt's previous statements that incoming EU students would not benefit from healthcare after the UK left the EU are also extremely damaging.
Erasmus exchanges are reciprocal. Receiving and guiding incoming students is complex and time-consuming; it's seen as worthwhile when staff know their own outgoing students are benefiting from mobility. Overstretched EU academic staff may well think twice about doing this work in the face of continued uncertainty and concerns about the UK's unwelcoming attitude to EU students.
The PR is indeed very bad.