Familia, working his third inning, hit Angels catcher Hank Conger with a bases-loaded, 2-2 fastball to bring in Raul Ibanez with the decider. It was Familia's 51st pitch of the game.
"You have to save [closer Jose] Valverde for a save if you get the lead, but you've got to have someone [John Lannan] behind him if the Angels come back and get a tie," Collins said. "You go three nights in a row with the starters going five innings, they [the relievers] are going to burn out.
"You don't want to have a guy go three innings. [Familia] did a nice job, we just didn't get him any runs."
Familia said Collins asked him if he was all right to pitch the 11th, and he said yes.
"I could keep pitching," Familia said. "I felt all right."
The Mets bullpen had run its scoreless innings streak to 18 1/3 innings before Ibanez opened the 11th with a single, advancing to third on a wild pitch and an infield out. Collins then had Familia intentionally walk Howie Kendrick and J.B. Shuck to bring up the Angels' reserve catcher.
"You either open up some holes with the infield in [and a runner at third], or you try to set up some force plays," Collins said. "You go down to the bottom of the lineup if you can, and Conger hasn't been playing much."
Mets starter Dillon Gee went 5 2/3 innings on 100 pitches but left with a 4-4 tie after giving up two homers and walking four.
"That's very uncharacteristic," Collins said of Gee's walks.
Carlos Torres was the first Mets reliever, and he did his specialty, getting four outs. He led the team with 15 such performances last year.
As the Angels threatened in the late innings, Torres was followed by Gonzalez Germen, Scott Rice, Kyle Farnsworth and then Familia in the ninth as Collins matched up against Mike Scioscia's lineup.
"[Familia] pitched his heart out," Torres said. "It's unfortunate the way it worked out. He hasn't done that at all [been extended], he hasn't built up for that."
A two-inning stint by Familia on Wednesday was his longest in three previous outings this season, with 22 pitches as his game high.
He said walking the bases loaded intentionally is "part of the game. Sometimes you have to do that.
"I was just trying to pound the zone [against Conger] and get a ground ball."
Conger said his approach to Familia "was to take it up the middle, get a ball in the air. Towards the end of that at-bat, his sinker was starting to work. He threw me a nasty one 2-1. Then he threw a fastball that was coming towards me, and I said, 'Get in there ... take one.'"
Travis d'Arnaud hit a long home run for New York, and Josh Satin, in his just his second start at first base, launched a two-run double, each connecting off Angels left-handed starter Tyler Skaggs.
The Mets took a 4-2 lead into the sixth, but Gee gave up a rare home run by Shuck. The two-run shot was Shuck's third homer in 521 career at-bats.
New York came into the game having not faced many left-handers -- just one starter previous to Skaggs -- and having little success against them. The Mets had a .314 team slugging percentage vs. lefties, with just three extra-base hits in 51 at-bats.
D'Arnaud boosted those numbers with his third-inning homer to left-center, getting the Mets even at 2-2. It was the young catcher's second Major League homer, coming 109 at-bats after he connected off Detroit's Rick Porcello on Aug. 25.
In the fourth, Curtis Granderson got his first hit off a lefty in 10 at-bats this season, and it was a double, setting up Mets at second and third for Satin. He delivered his first hit of the season after an 0-for-5 start, a two-run double for a 4-2 lead.
D'Arnaud started the season 0-for-15 at home, and there's nothing he can do about that mark until April 18, when the Braves visit Citi Field.
But his bat is coming to life on the road. He had two hits Tuesday at Atlanta and his first RBI the next night.
A Kendrick double and Chris Iannetta's two-out, RBI single put the Angels up 2-1 in the second. The Mets scored in the first on two singles and a double-play grounder, but Mike Trout equalized in the bottom of the inning with his third homer, a laser beam to left-center.
"I made a pitch [to Trout] I was actually trying to make," Gee said. "He's one of the best for a reason. You've got to tip your hat."