Captain Williams and striker McDonald both scored in the final home match of the season with Charlton which ended in a 2-2 draw - although the former's was an own goal.
Williams said: "We know what our failings have been, and hopefully they won't happen again.
"There'll be a lot of changes in the summer and I'm sure the gaffer has got his eye on players he feels can improve the squad.
"Finishing outside the play-offs is not the way we planned things and we can't deny it's hard to take. We have to dust ourselves down, get on with it and go again in August."
McDonald admitted: "It's been a difficult and frustrating season. As a squad, each of us has to ask questions of what we've done. Could we have done things differently? That's the question we have to answer."
Whilst Williams and McDonald look to next season in Boro colours, one man who will not be alongside them is Kireon Dyer.
The 34-year-old was signed on a short deal in January and he played in nine games, scoring twice.
But manager Tony Mowbray admits he is unlikely to be offered a return to the club.
"I don't think we'll be prolonging it to next season," Mowbray told the Evening Gazette when asked about Dyer.
"What I would say is that he's been a delight to work with. Not just on the field, off the pitch he's been fantastic; entertaining the players, bringing quizzes on the coach on a five-hour trip and being a good senior professional footballer for us and it's been good to work with him again."
Mowbray has also confirmed that the club's loan players - Sammy Ameobi, Josh McEachran and Ishmael Miller - will return to their parent clubs this week.
"I'm not officially sending them back," he said.
"But I'll have discussions with John Carver at Newcastle about Sammy and Stevie Holland at Chelsea about Josh. Ishmael picked up an injury and, with a week to go, he's probably going to go back to Nottingham Forest and meet his new manager."