Palace went behind after an impressive Lewis Wing strike and struggled to break down a resolute Boro defence as the game drew on. Despite a rather intense attacking onslaught, Hodgson's side ended the night as the losing team and must now return to south London to focus solely on their league campaign.
Speaking in his post-match press conference, Hodgson discussed the game in some depth.
Timing: "I don’t think it was too late because the whole of the second half we certainly got going and played some good football, but our first half performance wasn’t as good as it perhaps could or should have been.
"A lot of our possession in the first half was not threatening possession, whereas in the second half I thought we had a lot of possession, a lot of play in the opponent’s half and the final third of the field and I think we looked a lot more dangerous in that period of time."
Missed opportunities: "Of course it’s a missed opportunity, if that [Middlesbrough playing Burton Albion in the next round] is the case then even more so. The fact is it was a tight game, we always knew it would be a tight game. We didn’t think it would be a game with a lot of goals in it. We conceded one in the first half and that was rather unfortunate.
"[In] the previous two rounds, we’d done extremely well and won and tonight we missed an opportunity by not being able to win this game."
Changing the lineup: "Football today is a competition where you have a squad of players. We’ve had a fairly stable 11 this season and there were a lot of players there tonight who needed a game and they didn’t let me down in any shape or form. Furthermore, of the players we left at home, three of those [eight changed players] were injured.
"There were only four or five at home who possibly could have come - one of those being the keeper - so we pretty much used the players that we had at our disposal. The three players we actually spared are very important to us in other ways."
The opposition: "We're chasing a 1-0 deficit and playing against a team that obviously defends in numbers and defends well in their own penalty area so it wasn't easy to get any clear-cut chances that maybe would have given us an equaliser."
For more post-match reaction, head to Palace TV. Or, if you're reading in the app, click 'Palace TV'.