Evans was penalized but not ejected from the Saints' 30-10 victory.
Evans will miss Sunday's home game against the Jets.
Evans will appeal the suspension, a source told ESPN's Jenna Laine. Winston was pointing toward the Saints' sideline and repeatedly poked Lattimore's helmet. Mike Evans runs over to hit Lattimore, and a scuffle ensues.More news: Gunman opens fire at Texas church, killing at least 25
Evans, one of Tampa's top receivers, only caught 1 pass for 13 yards during the contest. Lattimore appeared to be involved in a verbal confrontation with the Buccaneers' sideline, and even got in a shoving match with Winston before Evans came over and threw punches.
Evans is still allowed to appeal the suspension and that could delay the enforcement pending a ruling from either National Football League commissioner Roger Goodell or an independent arbitrator. Jameis can not, under any circumstances, come off the sideline when he's not even playing in the game.
"If there's not an ejection in that situation, then I don't know when there's supposed to be an ejection", he said.More news: Trump says recalls little about meeting where aide mentioned Russian Federation
"The Saints player responded and then Mike responded".
Bucs coach Dirk Koetter said he didn't see the interaction or Evans' hit. I was glad he wasn't ejected. "That goes against everything you would want your team to stand for".More news: John Wall leaves arena with left arm in sling
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