Three days after losing to Mexico in a match that mattered, Jurgen Klinsmann’s U.S. national team will play Costa Rica in a game that does not matter. It feels like having to still go to class after taking the last exam of the semester. Except, in this case, the grade was a C and the professor won’t allow a re-take.

If this arrangement has an eerie feel to it, it’s because we went through the same thing in the summer: Gold Cup semifinal defeat followed by a third-place match.

On Tuesday night, the Americans will follow their CONCACAF Cup loss with a friendly against the Ticos at Red Bull Arena in Harrison, N.J. A small crowd is expected — fewer than 8,000 tickets sold as of Monday. Saturday’s setback at the Rose Bowl is only part of the reason; it’s a Tuesday, it’s a friendly and the important game, regardless of result, took place 72 hours earlier. You can’t blame New Yorkers and New Jerseyans for skipping this one.

Why was this game scheduled in the first place? In a week-long FIFA window, it’s foolish not to arrange two matches. If the CONCACAF Cup hadn’t been necessary, the U.S. Soccer Federation would have planned two friendlies. Mexico, too, will play a friendly Tuesday (Panama).

The listed start time is 6:30 ET, but kickoff is not until 7:07 on ESPN, UniMas and Univision Deportes.

As expected, Klinsmann made several roster changes. No matter how the Mexico game turned out, he was planning to allow some players to return to their clubs and invite fresh faces. In all, five joined the squad at training Monday in New Jersey while eight caught flights to various destinations.

In: D.C. United goalkeeper Bill Hamid, Orlando City defender-midfielder Brek Shea, New England Revolution midfielder Lee Nguyen, New York City FC midfielder Mix Diskerud and Sandhausen forward Andrew Wooten.

Out: Real Salt Lake goalkeeper Nick Rimando and midfielder Kyle Beckerman, Houston Dynamo defender DaMarcus Beasley, Sporting Kansas City defender Matt Besler and midfielder Graham Zusi, Toronto FC midfielder Michael Bradley, Seattle Sounders forward Clint Dempsey and San Jose Earthquakes forward Chris Wondolowski.

UPDATE: Klinsmann has dismissed Fabian Johnson from the squad. Johnson asked out of the Mexico match after 111 minutes but apparently was not injured. Klinsmann told reporters in New Jersey on Monday that he had a “severe word” with the Moenchengladbach defender.

Rimando and Beckerman have a critical MLS match Wednesday against the Portland Timbers. Bradley and TFC host the New York Red Bulls in an important Eastern Conference clash Wednesday. San Jose (Wondolowski) and Kansas City (Besler, Zusi) face one another Friday. Jozy Altidore was not released and will miss the Toronto match.

So the U.S. squad now stands at 21 players. Both Alejandro Bedoya, who missed Saturday’s match with illness, and Bobby Wood, his late roster replacement, remain on the list.

After 120-minute runs against Mexico, Geoff Cameron and Jermaine Jones seem unlikely to play against Costa Rica. Johnson went 111 minutes before running out of gas, Altidore 98 and Gyasi Zardes 78.

Goalkeeper Tim Howard is a good bet to make his first appearance since returning from a one-year leave. DeAndre Yedlin and Wood, the subs who combined for the extra-time equalizer, are prime candidates to start.

Unlike the CONCACAF Cup, which restricted Klinsmann to three substitutes, friendlies allow for six in-game moves.

Costa Rica lost at home to South Africa, 1-0, on Thursday. Oscar Ramirez’s squad includes Real Madrid goalkeeper Keylor Navas, West Brom defender Cristian Gamboa, Everton defender Bryan Oviedo, Deportivo de La Coruna midfielder Celso Borges, Arsenal forward Joel Campbell and two MLS players: Vancouver Whitecaps defender Kendall Waston and Montreal Impact midfielder Johan Venegas.

Updated U.S. roster

Goalkeepers: Brad Guzan (Aston Villa), Bill Hamid (D.C. United), Tim Howard (Everton).
Defenders: Ventura Alvarado (Club America), Geoff Cameron (Stoke City), Brad Evans (Seattle Sounders), Fabian Johnson (Moenchenglandbach), Michael Orozco (Tijuana), Tim Ream (Fulham), Jonathan Spector (Birmingham City).
Midfielders: Alejandro Bedoya (Nantes), Mix Diskerud (New York City FC), Jermaine Jones (New England Revolution), Lee Nguyen (New England Revolution), Brek Shea (Orlando City), Danny Williams (Reading), DeAndre Yedlin (Sunderland).
Forwards: Jozy Altidore (Toronto FC), Bobby Wood (Union Berlin), Andrew Wooten (Sandhausen), Gyasi Zardes (L.A. Galaxy).

My unscientific lineup prediction:

Howard

Evans, Alvarado, Orozco, Ream

Yedlin, Williams, Diskerud, Shea

Wood, Wooten