The three men had been enjoying the sunshine during lockdown when they were attacked by Saadallah, who had set out to kill as many people as he could.
Three others, Stephen Young, and Patrick Edwards and Nishit Nisudan, were all knifed by Saadallah but survived the attack in Forbury Gardens, Reading.
Saadallah was sentenced, in January, to life in prison for each of the murders, with a whole life tariff, and concurrent jail sentences of 24 years for the three attempted murders.
On Thursday, Saadallah appeared at the Court of Appeal in London via video-link from Belmarsh Prison, wearing a dark jumper, to challenge the length of his sentence.
However, after a hearing, the Lord Chief Justice Lord Burnett, sitting with Mrs Justice Cheema-Grubb and Mr Justice Henshaw, said his challenge had been unsuccessful.
Lord Burnett said: "We have concluded that there is no substance in any of the criticisms made of the judge's conclusions. In these circumstances we refuse leave to appeal."