Chris Froome finished the Tour de l'Ain 26 minutes behind Tour de France rival and Ineos team-mate Egan Bernal.
Bernal finished second in the race, 18 seconds behind winner Jumbo-Visma's Primoz Roglic, with Froome 41st.
The race across the l'Ain region of France is the second of three crucial races which will decide who will be selected by Ineos for the Tour, which begins on 29 August.
The final race is the Criterium du Dauphine on 12 August.
Roglic won Sunday's final stage of the three-day event up the Grand Colombier climb, four seconds ahead of Bernal and six seconds ahead of Arkea-Samsic's Nairo Quintana.
Slovenian Roglic's win caps an eventful week for Jumbo-Visma, who won Saturday's Milan-San Remo one-day 'monument' race and last Saturday's Strade Bianche through Wout van Aert.
Their sprinter Dylan Groenewegen was also involved in the horrifying crash which left Fabio Jakobsen in a coma and requiring plastic surgery to his face during a sprint at the end of the first stage of the Tour of Poland on Wednesday.
Jakobsen's team-mate Remco Evenepoel won the Tour of Poland, with Britain's Simon Yates of Michelton-Scott third.
Bernal's Ineos team-mates and fellow former Tour de France winners Geraint Thomas and Froome both lost time on Saturday, with the Welshman finishing over four minutes back on Roglic and Froome particularly struggling, losing 12 minutes.
Froome, 35, and Thomas worked as domestiques to support Bernal, 23, on Sunday's stage to help fight for victory.
Froome, who will join Israel Start-Up Nation at the end of the season, finished nearly 10 minutes behind race winner Bernal at last week's Route d'Occitanie.
BBC Sport's Matt Warwick
It's not looking good for Froome. What, in normal circumstances, would be mere warm-up races for the four-time Tour winner are, in the post lockdown sporting world, now a shoot-out with Bernal to see who goes to this year's Tour.
The reason? Team Ineos will probably not want to take all three of their former Tour winners - Froome, reigning champion Bernal and 2018 winner Thomas - to avoid too complex a dynamic interrupting their metronomic progress up the climbs during cycling's greatest race.
Bernal is in fine form, having won the first race and commanding a supporting role from Thomas during this race - setting an agenda for the Tour that Froome can only interrupt by beating Bernal in next week's Dauphine.
And it was the Dauphine last year which started Froome's troubles, when he had his horrifying crash and from which he is still trying to fight back to top form.
That form was improving on Sunday. Just as well - this coming week will define Froome's year.
Tour de l'Ain stage 3 result
1. Primoz Roglic (Slo/Team Jumbo-Visma) 4hours 6mins 24secs
2. Egan Bernal (Col/Team Ineos) +4secs
3 Nairo Quintana (Col/Team Arkea Samsic) +6secs
4. Guillaume Martin (Fra/Cofidis) +8secs
5. Richie Porte (Aus/Trek-Segafredo) same time
6. Steven Kruijswijk (Ned/Team Jumbo-Visma) +23secs
Selected other: 30. Chris Froome (GB/Team Ineos) +12mins 16secs
Tour de l'Ain general classification
1. Primoz Roglic (Slo/Team Jumbo-Visma) 11hours 21mins 12secs
2. Egan Bernal (Col/Team Ineos) +18secs
3 Nairo Quintana (Col/Team Arkea Samsic) +28secs
4. Steven Kruijswijk (Ned/Team Jumbo-Visma) +56secs
5. George Bennett (NZ/Team Jumbo-Visma) +1min 27sec
6. Bauke Mollema (Ned/Trek-Segafredo) +2min 24secs
Selected other: 41. Chris Froome (GB/Team Ineos) +26mins 45secs