Evan Longoria homered and collected three hits while Red Sox starter Daisuke Matsuzaka was touched for four runs in his 2009 debut.
"Jacoby runs the count deep, [but] he can't get on," said Francona. "Petey scalds the ball, [but] Longoria makes a great play. Again, we gave ourselves a chance. We came up short, but we gave ourselves a chance.
"With David coming up and having Youkilis swinging the way he's swinging, you'd rather go into the ninth, obviously, with the lead, but we'll take those guys hitting."
The events that led up to that final at-bat sum up the frustration of the day for the Red Sox. After Ellsbury flew out to center, Pedroia scorched a one-hopper to the left of Longoria at third. Longoria, with eyes not fully open, snared it and threw on to first for the second out.
"It's one of those games where not a lot of balls bounced our way," Pedroia said. "They hit a couple of home runs in key spots and we gave ourselves a chance in the end, and that's a good sign, especially this early in the season."
Things really looked promising when Youkilis came up as the winning run following the walk to Ortiz. Youkilis was 3-for-3 with a walk and was hitting .727 going into the at-bat.
But this time it wasn't meant to be, as Youkilis squared up the ball but it was hit to the worst part of the park -- as far as the Red Sox were concerned -- as Gabe Kapler hauled it in for the final out.
In his first start of the season, Matsuzaka (0-1) allowed four runs and three homers over 5 1/3 innings, allowing nine hits and three walks while striking out five. He threw 100 pitches, 60 for strikes, on the day.
From the start, it was apparent that the World Baseball Classic MVP didn't have his command. After retiring the first two batters in the first, Matsuzaka allowed a sharp double past a diving Mike Lowell at third. Dice-K then walked Carlos Pena before striking out Willy Aybar looking to end the threat.
Matt Joyce opened the second with the first of three homers on the day off Matsuzaka, a towering drive to the first row of seats beyond the Rays' bullpen.
Longoria belted a two-run homer to the third row of Green Monster Seats in the third, while Shawn Riggans belted an opposite-field homer to right-center with one out in the fourth to put Tampa Bay ahead, 4-0.
"I thought overall [Matsuzaka] was pretty good," Varitek said. "The way Evan is swinging the bat, you don't get away with many mistakes, and I think that was the biggest mistake of all of them. He was able to keep us in that game with not his best stuff overall. It allowed us to battle back. He left us in that game."
"The mistakes really hurt him," Francona added. "A breaking ball to Longoria caught too much of the plate, and [so did] a first-pitch fastball to Riggans. I know there were a lot of baserunners in between -- a lot of them -- but those were their runs."
The Red Sox finally got to Tampa Bay starter Matt Garza (1-0) in the sixth, as Jason Bay's one-out triple scored Youkilis with Boston's first run. Garza allowed just four hits and one run over seven innings to earn his first win of the season.
Youkilis collected three hits on the day and is batting .667 in his first three games.
With the tying runs in scoring position following an RBI double by Mike Lowell, Joe Nelson struck out Jed Lowrie to end the eighth.
Varitek made things interesting in the ninth with a leadoff homer against Percival, but the Rays' closer would settle down and nail down his first save.
"We're trying to get the tying run to the plate -- hopefully the winning run," said Francona. "[Varitek] had hit into some tough luck the last couple of days. He got enough of it to get it out of there and give us a chance."