Bamford scored 17 top-flight goals in an outstanding Premier League campaign and was watched by Southgate in the recent home game with Spurs, when he found the net.
The only English-born player to score more times than Bamford in the top flight in 2020-21 was Harry Kane.
But despite all that, the forward has missed out on a place in Southgate's 33-man provisional squad for the finals.
Southampton frontman Danny Ings was also not included in the squad, with a training camp to be held at Middlesbrough's training ground on the borders of North Yorkshire and County Durham ahead of two friendlies against Austria and Romania at the Riverside Stadium prior to the tournament.
England open up in Group D against Croatia at Wembley on June 13 and host old enemy Scotland at the home of football five days later before entertaining the Czech Republic on June 22.
Kane, Dominic Calvert-Lewin, Marcus Rashford, Raheem Sterling and Ollie Watkins have all been chosen ahead of Bamford, who was also overlooked for the Three Lions' three games in the last international break against Poland, Albania and San Marino in World Cup qualifiers.
"I think we've probably looked at the squad in March, the basis of this squad we had in March and we were very pleased," said Southgate.
"The forwards we've selected were with us in March. There's Danny (Ings) and Patrick Bamford who have had very good seasons - I've said that before.
"But we didn't see any reason to change those positions from the players that did well for us in the games, the three qualifiers we won in March."
Bamford's team-mate Kalvin Phillips has been chosen in the squad, but his fitness will be assessed this week after he picked up a shoulder injury late on in Leeds's 3-1 home win over West Brom on the final day of the season on Sunday.
Phillips, Harry Maguire, Jordan Henderson and Nick Pope are all to be assessed over the coming days due to injury issues, with Southgate set to therefore wait until June 1 before naming his final 26 for the finals.
He added: "Kalvin Phillips was injured in the 93rd minute on Sunday, we'll know more about that and it's severity and possible timelines in the next few days.
"He (and Harry Maguire) are part of the reason why we've done this (naming a provisional 33-man England squad)."