Before Sunday's game, Francona was in Valentine's office, along with fellow ESPN broadcasters Dan Shulman and Orel Hershiser, to do their standard pregame session with the manager.
That session was said to be cordial and comfortable by people who were in the room.
"Oh, I yelled at him as soon as he came into my office and said, 'Don't ever do that again.' No, I said, 'Hey, how you doing?' We didn't bring it up," said Valentine.
Boston's current manager downplayed the presence of his predecessor in the clubhouse on Saturday.
"I didn't think it was any big deal," Valentine said. "I didn't see it. I wasn't there partaking in the conversation but what's the big deal?"
Francona and the Red Sox parted ways last year after the team was eliminated from the playoffs on the final day of the regular season. Valentine replaced Francona, and under his watch this year the Red Sox have underperformed expectations at 50-51.
They began the day 10 1/2 games behind the first-place Yankees in the American League East after splitting the first two games of the three-game weekend series, Boston's first in New York this season.
When asked about it on Sunday, Francona would neither confirm nor deny that he sent the text message.
"That's personal," Francona said. "I don't talk about my text messages."
Valentine has been in the eye of the storm all season, his first managing in the Major Leagues since a seven-year tenure with the Mets ended in 2002.
After the Red Sox lost the opener on Friday night, 10-3, Francona entered the clubhouse on Saturday initially speaking to Cody Ross, but he also ended up talking to Pedroia. Clay Buchholz, Jarrod Saltalamacchia, Nick Punto and David Ortiz were among those who joined the group.
Valentine was in his office with the door closed as this transpired and was advised later of Francona's presence.
"We've got drama," Valentine said after Saturday's game that the Red Sox won, 8-6, with two runs in the top of the ninth. "We've got pregame drama, we've got in-game drama, and we've got postgame drama. Man, we've got drama."