They will, winning EL might be easier then ending top 4 in EPL (Chelsea will eventually bounce back, the two Manchester teams are better and who knows a team like Tottenham might surprise them this year) and winning EL also gives you a CL spot.
Last year Tottenham and Liverpool showed their motivation in EL, as well as WH and Southampton this season. CL spot didn't motivate them that much so how can it motivate Big 4? I don't think they will have any problems ending top 4 in EPL. As EPL fans say "BPL title is most important title".
Can someone explain please, why EPL had 8 teams in Europe this season?